Find the volume of a sphere with a great circle area of 201.06 square inches

Answers

Answer 1

assuming you meant a "circular cross-section" of 201.06 in².

so, we know if we cut the sphere like a cantaloupe, in half, the circular inner-part of the cantaloupe will have an area of 201.6 in².

keeping in mind that, the radius of that circular section, is the same radius of the sphere, what is it anyway?

[tex]\bf \textit{area of a circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\ -----\\ A=201.06 \end{cases}\implies 201.06=\pi r^2 \\\\\\ \cfrac{201.06}{\pi }=r^2\implies \sqrt{\cfrac{201.06}{\pi }}=r\\\\ -------------------------------[/tex]

[tex]\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}\qquad \qquad \implies V=\cfrac{4\pi \left( \sqrt{\frac{201.06}{\pi }} \right)^3}{3}\implies V=\cfrac{4\pi \left( \frac{\sqrt{201.06^3}}{\sqrt{\pi ^3}} \right)}{3} \\\\\\ V=\cfrac{4\pi \cdot \frac{\sqrt{201.06^3}}{\pi \sqrt{\pi }}}{3}\implies V=\cfrac{\frac{4\sqrt{201.06^3}}{\sqrt{\pi }}}{3}\implies V=\cfrac{4\sqrt{201.06^3}}{3\sqrt{\pi }}[/tex]

Answer 2

Final answer:

To find the volume of a sphere with a given great circle area, solve the equation 4πr² = 201.06 to find the radius, then use the formula V = (4/3)πr³ to calculate the volume. The volume is approximately 267.97 cubic inches.

Explanation:

To find the volume of a sphere with a given great circle area, we first need to find the radius of the sphere. The great circle area is equal to the surface area of the sphere, which is 4πr², where r is the radius of the sphere. In this case, the great circle area is 201.06 square inches, so we can solve the equation 4πr² = 201.06 to find the radius. Once we have the radius, we can use the formula for the volume of a sphere, V = (4/3)πr³, to calculate the volume.

First, let's solve the equation 4πr² = 201.06 for r:

4πr² = 201.06

r² = 201.06 / (4π)

r² ≈ 16.06

r ≈ √16.06 ≈ 4.01

Now that we have the radius, we can calculate the volume using the formula V = (4/3)πr³:

V ≈ (4/3)π(4.01)³ ≈ 267.97 cubic inches

Related Questions

HELP, MARKING BRAINLIEST
How many compass settings are required to complete the construction?

Answers

C) 3
Hint: if you don't know the answer you can count the number of arcs

C) 3 Hope this helps

Any help I don’t really understand this

Answers

Comment
The point is how to remove the brackets when a minus sign is on the left hand side. A second problem is how to get all the terms on one side over to the other.

Step One
Remove the brackets on the left side. This is an absolutely necessary step in the rest of your mathematical studies. What was done in this step affects all three terms on the inside of the brackets. Minus signs are real bad things to misuse. Study carefully how to change the signs when multiplying by a minus.

Rule a minus sign outside the brackets, when multiplied by anything inside the brackets, change the sign to the opposite of what it was.

-20 + 4x + 5x^2 = 20 - 7x^2

Comment
Before doing the last step, look at the answers. Two of them are 40. That is the answer for 20 and -20 when transferred. It's 40 which is a plus. So you should be transferring from left to right.

Step Two
Transfer from left to right.
-20 + 4x + 5x^2 = 20 - 7x^2 Add 20 to both sides.
4x + 5x^2 = 20 + 20 - 7x^2 Subtract 4x from both sides.
5x^2 = 40 - 7x^2 - 4x Subtract 5x^2 from both sides
0 = 40 - 7x^2 - 5x^2 - 4x
0 = 40 - 12x^2 - 4x Now you have to put them in the right order.

0 = 40 - 4x - 12x^2 <<<<< Answer

1.)Simplify the expression: 4 times Start Root 18 End Root plus 5 times Start Root 32 End Root

2.)Simplify the expression: 7 times Start Root 5 End Root minus 3 times Start Root 80 End Root

3.)Simplify the expression: Start Root 21 End Root times Left Parenthesis Start Root 3 End Root plus Start Root 14 End Root Right Parenthesis.

4.)Simplify by rationalizing the denominator: Start Fraction 4 over Start Root 10 End Root minus Start Root 6 End Root End Fraction

I WILL MAKE YOU THE BRAINIEST! PLEASE HELP

Answers

1.) 32 start root 2 end root

2.) -5 start root 5 end root

3.) 3 start root 7 end root + 7 start root 6 end root

4.) start root 10 end root + start root 6 end root

hope this helped :)

Answer:

I agree with Sydneyjones :D i very much agree

1.) 32 start root 2 end root

2.) -5 start root 5 end root

3.) 3 start root 7 end root + 7 start root 6 end root

4.) start root 10 end root + start root 6 end root

what is the quotient of 15p^-4q^-6/-20^12q^-3 in simplified form

Answers

The first step for solving this problem is to reduce the fraction with [tex] q^{-6} [/tex].
[tex] \frac{15p^{-4} }{-20^{12} q^{3} } [/tex]
Determine the sign of the fraction.
[tex] -\frac{15p^{-4} }{20^{12} q^{3} } [/tex]
Now if a negative exponent is in the numerator,, then you must move the expression to the denominator and then make the exponent positive. This will change the expression to the following:
[tex]- \frac{15}{ 20^{12} q^{3} p^{4} } [/tex]
Lastly,, use the commutative property to reorder the terms on the bottom of the fraction.
[tex]- \frac{15}{ 20^{12} p^{4} q^{3} } [/tex]
Since we cannot simplify this expression any further,, the correct answer to this question is [tex]- \frac{15}{ 20^{12} p^{4} q^{3} } [/tex].
Let me know if you have any further questions.
:)

The simplified form of the expression: [tex]$ -\frac{15}{2^{24} \times 5^{12} \times p^4 \times q^3} $[/tex]

To simplify the expression [tex]$ \frac{15p^{-4}q^{-6}}{-20^{12}q^{-3}} $[/tex], we can apply the rules of exponents and simplify each part of the expression separately.

First, let's rewrite [tex]$ -20^{12} $ as $ -(20^{12}) $[/tex] to make it clear that the exponent applies to the entire term:

[tex]\[ \frac{15p^{-4}q^{-6}}{-(20^{12}q^{-3})} \][/tex]

Now, let's simplify each part:

1. $ p^{-4} $ can be rewritten as [tex]$ \frac{1}{p^4} $.[/tex]

2. $ q^{-6} $ can be rewritten as [tex]$ \frac{1}{q^6} $.[/tex]

3. [tex]$ 20^{12} $[/tex] can be calculated.

[tex]\[ \frac{15}{-(20^{12})} \times \frac{1}{p^4} \times \frac{1}{q^6} \times \frac{1}{q^{-3}} \][/tex]

Now, let's calculate [tex]$ 20^{12} $:[/tex]

[tex]\[ 20^{12} = (2^2 \times 5)^{12} = 2^{24} \times 5^{12} \][/tex]

[tex]\[ = (2^4)^6 \times 5^{12} = 2^{24} \times 5^{12} \][/tex]

Now, we can rewrite the expression:

[tex]\[ \frac{15}{-(2^{24} \times 5^{12})} \times \frac{1}{p^4} \times \frac{1}{q^6} \times \frac{1}{q^{-3}} \][/tex]

[tex]\[ = -\frac{15}{2^{24} \times 5^{12} \times p^4 \times q^6 \times q^{-3}} \][/tex]

[tex]\[ = -\frac{15}{2^{24} \times 5^{12} \times p^4 \times q^3} \][/tex]

This is the simplified form of the expression.

need help for question one in polynomials

Answers

Answer:

a) monomial
b) constant
c) binomial
d) trinomial
e) binomial
f) constant
g) monomial

Step-by-step explanation:

Let's start by defining the terms in the question:
A monomial is an expression with a single term, regardless of how many variables are in the term.
A binomial is an expression with two different terms, which cannot be combined into a single term due to their variables not matching.
A trinomial is an expression with three different terms, which cannot be combined into a binomial or monomial because their variables do not match.
A constant is an integer that lacks a variable attached to it. An integer with a variable attached to it would be a monomial, and the integer itself would be called a coefficient.

Now, we can get into the parts of the question:
a) 8a²b is two variables however it is still a single term so this is a monomial.

b) -39 is an integer with no variables attached. Therefore, it is a constant.

c) x + y is two variables and two different terms that cannot be combined into one single term. It is a binomial.

d) -12xy + 5y - x² showcases three different variables and three different terms that cannot be consolidated. Thus, it is a trinomial.

e) 2x² + 2y² demonstrates two different variables and two different terms that are not alike. As such, we have a binomial.

f) 3/4 is an integer with no variables in sight. We have here a constant.

g) -32m²n² has two variables but is only a single term on its own. This is a monomial.

Which of the following shows that polynomials are closed under subtraction when polynomial 5x − 6 is subtracted from 3x2 − 6x + 2?

A) 3x2 − 11x + 8 may or may not be a polynomial
B) 3x2 − 11x + 8 will be a polynomial
C) 3x2 − x + 4 may or may not be a polynomial
D) 3x2 − x + 4 will be a polynomial

Tip: Every 2 after 3x is an exponent.. so it would be 3x^2

Answers

Answer: Choice B
3x^2 - 6x + 2 will be a polynomial

======================================

Explanation:

Line up the terms and subtract straight down
3x^2 - 6x + 2
5x - 6
-----------------
3x^2 -11x + 8

this is a polynomial as it is a sum of three monomials

Subtraction of any two polynomials will result in another polynomial. This is what closure means. In math terms, closure is the idea of taking two objects and performing some operation on them (eg subtraction). If we get the same type of object back, then the set of considered closed under that operation.

Here's another example of closure. Take two glasses of water and pour them together. The two glasses can be of different shapes and sizes. It doesn't matter. The fact that we have two containers of water is all that matters. In this example,the water is like the polynomial. Combining the two containers of water into one will result in a greater amount of water. Combining water with water leads to more water.

HELPPPPPPPPPP and explain

Answers

There is so much controversy about this question on the internet (well not this question exactly but the idea of taking a reciprocal of a discontinuous function).

Some say you can if you make it clear that the point causing the trouble is excluded in some way. Others say that you cannot contemplate the idea. You are creating a meaningless situation with no definition. It really depends on what you have been told about division by 0. There are ways of getting around this, but you are not taking a calculus course and therefore you likely don't have the tools to deal with it. In any event, it does not look to me like you know about limits yet.

Your marker or teacher or tutor can go either way on this problem and be justified in marking you wrong no matter what you do. As instructed I will put what I think should be done in the comment section. And remember, I'm counting noses and going with the majority when I answer this. It's not anything I'm 100% certain of, but neither is anyone else.

The health care Jimmy’s employer offers is a fee-for-service plan in which Jimmy and his family must pay for $12,500 in health related services in a calendar year before the insurance company begins to pay. Jimmy and his family have several health related issues that demand $685.00 each month. If one of Jimmy’s children were to become seriously injured at the end of the year, how much more would Jimmy and his family need to pay before the insurance company begins to assume responsibility?
a.
$984.58
b.
$4,280.00
c.
$11,815.00
d.
$14,417.92

Answers

The answer is Letter B - $4,280.00.

Total the amount they could incur because of health issues in a year then deduct it from 12,500.

= 685 x 12 months
= 8,220; they incur $8,220 for their health related issues in a year

= 12,500 - 8,220
= 4,280; amount they need to pay before the insurance company assumes responsibility.

What is a correct first step in solving the inequality –4(3 – 5x)≥ –6x + 9?

Answers

use the distributive property to simplify the left side

-12 + 20x >= -6x + 9

In order to solve the inequality, You need to work the parenthesis, -4(3-5x)>-6x=9.
-12+20x>-6x+9
-12+26x>9
26x>21
Now divide both sides by 26, and the answer is:
Answer: x is greater than or equal to 21/26 (21 over 26)

What is the exact value of cos 30° ?

Answers

Consider a ΔABC in which ∠ C = 90°, ∠A = 60° and ∠ B = 30°.

Side AB will be the hypotenuse.

cos 60° = AC / AB -------[ cos 60° = 1/2]

So, AB = 2 AC -------------------------------(1)

Apply Pythagorean Theorem to find BC

AB² = BC² + AC²

4 AC² = BC² + AC²

So, BC = √3 AC ------------------------(2)

Now, we shall find the value of cos 30°

cos 30° = CB / AB

or, = √3 AC / 2 AC -------using equations (1) and (2)

So, cos 30° = √3 / 2

Hence, the exact value of

Since ∠A = 2∠B. So, cos 30° will be √3 / 2

The answer is √3 / 2

The cost function for kara's new clothing store where she sells t-shirts is c = $9.90n + 1060. what is the slope of the cost function for kara's new store?

Answers

Remember that in a linear function of the form [tex]y=mx+b[/tex], the slope, [tex]m[/tex], is the coefficient of the independent variable [tex]x[/tex].

In our cost function [tex]c=9.90n+1060[/tex], [tex]y=c[/tex] and [tex]x=n[/tex], so we can infer that the independent variable is [tex]n[/tex]. Since the coefficient of [tex]n[/tex] is 9.90, the slope of the cost function is 9.90.

We can conclude that the slope of Kara's new store cost function is $9.90

Answer:

The slope of the function is 9.90

Step-by-step explanation:

You can find the slope by looking at the coefficient of the independent variable in the equation. In this case, we would be looking for the coefficient of n.

Consider a single spin on the spinner shown below. Which events are mutually exclusive? Check all that apply.

landing on an unshaded portion and landing on 2
landing on a shaded portion and landing on 3
landing on a shaded portion and landing on an even number
landing on an unshaded portion and landing on a number greater than 3
landing on a shaded portion and landing on an unshaded portion

Answers

Answer:

Options A, B and E represent mutually exclusive events.

Step-by-step explanation:

Two events are mutually exclusive that can not happen at a same time.

Now let us look at our options and find which statements represent mutually exclusive events.

A. We can see that landing on an unshaded portion and landing on 2 are mutually exclusive events as unshaded portion contains 3 and 4 and 2 lies on shaded portion.

B. Landing on a shaded portion and landing on 3 is also mutually exclusive as 3 lies on unshaded portion.

C. Landing on a shaded portion and landing on an even number can happen at the same time as 2 is an even number and it lies on shaded portion.

D. Landing on an unshaded portion and landing on a number greater than 3 can happen at the same time as 4 in greater than 3 and it lies on unshaded portion.

E. Landing on a shaded portion and landing on an unshaded portion are mutually exclusive events as spinner can be either in shaded portion or in unshaded portion.

Therefore, Options A, B and E are our correct choices.

Answer:

A, B, E

Step-by-step explanation:

I just did it on edge and got it right

Two angels re supplementary. The larger angle is 48 degrees more than the 10 times the smaller angle. Find the measure of each angle.

Answers

Supplementary angles are two angles that add up to 180°.

STEP 1:
find the value of x

x= smaller angle
10x + 48= larger angle

Add the two angles above to equal 180.

x + (10x + 48)= 180
combine like terms

11x + 48= 180
subtract 48 from both sides

11x= 132
divide both sides by 11

x= 12° smaller angle

STEP 2:
find the value of the second angle

=10x + 48
=10(12) + 48
=120 + 48
=168° larger angle

CHECK:
12° + 168°= 180°
180°= 180°

ANSWER: The smaller angle is 12° and the larger angle is 168°.

Hope this helps! :)

The tree diagram shows Pam’s choices for her appetizer and a meal at a restaurant. How many choices include chicken

Answers

There is no tree diagram?

Answer is 8, i just did it

List the following stocks and bonds in order from lowest default risk to highest default risk:

Bond in a stable foreign government
Preferred stock
Common stock

A. foreign government bond, common stock, preferred stock

B. foreign government bond, preferred stock, common stock

C. common stock, preferred stock, foreign government bond

D. preferred stock, common stock, foreign government bond

Answers

You have a government bond when a government bond issues a direct obligation.
Common and preferred stock both represent the ownership of a corporation, but preferred stockholders are paid before common stockholders, both in good and bad times.

Therefore, from least to highest default risk we have a bond in a stable foreign government, preferred stock and then, common stock.

Hence, the correct answer is B. foreign government bond, preferred stock, common stock.

ommy Teacher wants to analyze the weights of the students at his school. He knows the weight of the students is normally distributed so he can use the standard normal distribution. He measures the weight of 100 randomly selected students in the school. He finds the mean is 80 pounds and the standard deviation is 8 pounds.

Out of 100 students, how many should weigh between 64 and 96 pounds?

Answers

We first determine the z-scores for the given x-values of 64 and 96.
For x = 64: z = (64 - 80) / 8 = -2
For x = 96: z = (96 - 80) / 8 = 2
Therefore we find the probability that -2 < z < 2, which is around 0.95. Therefore, out of 100 students, approximately 100(0.95) = 95 students will weigh between 64 and 96 pounds.

The area of a piece of construction paper is 204 inches. The paper is 17 inches long. What is the width of the paper?

Answers

The width of the construction paper is 12 inches.

The formula for area is length(l)*width(w)=area in units squared(a^2).

To find the width, we divide both sides by length, this gives us the following:

17*w=204in^2 w=204in^2/17

To find the answer, you just perform the operation.

204/17=12

The width is 12 inches.

the amount that results when $4000 is compounded at 6% annually over seven years

Answers

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\to &\$4000\\ r=rate\to 6\%\to \frac{6}{100}\to &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{annually, thus once} \end{array}\to &1\\ t=years\to &7 \end{cases} \\\\\\ A=4000\left(1+\frac{0.06}{1}\right)^{1\cdot 7}\implies A=4000(1.06)^7[/tex]

What is the approximate difference in the growth rate of the two populations? The approximate difference in the growth rate is 10 percent. The approximate difference in the growth rate is 40 percent.

Answers

B IS THE ANSWER HOPE THIS HELPS

Answer:

Step-by-step explanation:

The approximate difference in the growth rate is 40 percent.

In bridge each player is dealt a hand of 13 cards from a deck of 52 cards. there are 4 aces in the entire deck. what are the expected number of aces in a single hand of cards?

Answers

P(ace card) = 4/52 = 1/13

Expected number of aces in a single hand of cards = 1/13 x 13 = 1

Answer: 1 ace card

One ace card is the answer

jack paid $2.60 sales tax on a $52 pair of shoes that he purchased. how much sales tax will his friend pay if his friend purhases a $28 shirt?

Answers

$2.60 is 5% of $52 because: 2.6 ÷ 52 = 0.05(5 %)

5% = 0.05

Find 5% of $28:

0.05 × 28 = 1.4

Answer = His friend will pay $1.40 for sales tax

Hope this helped☺☺

Does anyone know anything about The Distributive property? Please help!

Answers

when you distribute by multipling

El área de un rectángulo es 675cm2, si el largo es 3 veces. ¿Cuáles son las dimensiones del rectángulo?

Answers

The answer is 15 cm. Hope I could be of help! ; )

Add. Express your answer in lowest terms. 8 3/10 + 7 2/15

Answers

[tex]8 \dfrac{3}{10} + 7 \dfrac{2}{15} [/tex]

[tex]= 8 \dfrac{9}{30} + 7 \dfrac{4}{30} [/tex]

[tex]=15 \dfrac{13}{30} [/tex]

Final answer:

To add 8 3/10 and 7 2/15, we need to find a common denominator. The sum is 15 1/15.

Explanation:

To add 8 3/10 and 7 2/15, we need to find a common denominator. The least common multiple of 10 and 15 is 30. So we convert both fractions to have a denominator of 30: 8 3/10 = 8 9/30 and 7 2/15 = 7 4/30. Now we can add the whole numbers and the fractions separately:

8 + 7 = 159/30 + 4/30 = 13/30

Combining the results, the sum is 15 13/30. To express the answer in lowest terms, we can simplify the fraction: 13 and 30 are both divisible by 13, so dividing both by 13 gives us 1 and 2/30. Therefore, the final answer is 15 2/30, which can be further simplified to 15 1/15.

HELP ME PLS BBRAINLIESST AND 10 POINTS

Answers

p(not like black | not like pink) = 9/32 ≈ 28.1%

Look on the row for "not like pink". Your probability is the number under "not like black" divided by the total for "not like pink".

A 12.0-cm segment makes a 108.0-degree angle with a 16.0-cm segment. To the nearest tenth of a cm, find the third side of the triangle determined by this SAS information.

Answers

Begin by using the cosine rule to find the unknown side.

Where a- unknown side, b is 12, c is 16 and angle in between is 108°

The cosine rule...

a² = b² + c² - 2bc cosA

= 12² + 16² - (2×12×16 cos108°)

= 518.655076

Taking the positive square root...

a = 22.774

a = 22.8 cm nearest tenth

Final answer:

The question involves finding the length of the third side of a triangle using the Law of Cosines. The known parameters are two sides and the included angle. The formula c² = (12 cm)² + (16 cm)² - 2*(12 cm)*(16 cm)*cos(108 degrees) can be used to calculate the length of third side.

Explanation:

In this problem, you're dealing with a triangle and need to find the length of the third side. This is a classic case of using the Law of Cosines - a geometric rule that helps you find the length of a side of a triangle when you know the lengths of the other two sides and the angle in between (or in this case, SAS information).

The Law of Cosines formula is: c² = a² + b² - 2ab*cos(C), in which 'a' and 'b' represent the sides of the triangle adjacent to angle 'C', and 'c' is the other side. In your case, 'a' is 12.0 cm, 'b' is 16.0 cm and angle 'C' is 108.0 degrees. The third side 'c' can be calculated accordingly.

So, in this scenario, c² = (12 cm)² + (16 cm)² - 2*(12 cm)*(16 cm)*cos(108 degrees). With some basic arithmetic and the use of a calculator to compute the cosine, you can determine the length of the third side, 'c', to the nearest tenth of a cm.

Learn more about Law of Cosines here:

https://brainly.com/question/21634338

#SPJ3

Marilyn uses a credit card with a 19.9% APR compounded monthly to pay for car repairs totaling $991.38. She can pay $410 per month on the card. What will the total cost of this purchase be?

$1,021.01

$1,188.66

$991.38

$1,192.39

Answers

Marilyn's finance charge at the end of the first month will be
$991.38 × 0.199/12 = $16.44
The balance subject to the next month's finance charge will be
$991.38 +16.44 -410.00 = $597.82

The finance charge at the end of the second month will be
$597.82 × 0.199/12 = $9.91
The balance remaining after the second payment will be
$597.82 +9.91 -410.00 = $197.73

The finance charge applied at the end of the third month is
$197.73 × .199/12 = $3.28
so Marilyn can make one final payment of
$197.73 +3.28 = $201.01
to pay off the balance.

In all, Marilyn has paid 2×$410.00 +201.01 =
$1021.01 . . . . . . . . corresponds to the first choice

_____
In real life, Marilyn's credit card may not accrue any finance charge until after the first statement on which the charge appears. Thus the total cost of the purchase may be only $1004.02. The attached spreadsheet shows the beginning balance and the finance charges for each month for the two different scenarios.

A string of christmas tree lights has 15 lights what is the probability that the defective light is the 3rd from the plug

Answers

it will be 3:15 the 3rd plug over all 15 lights

What is the total number of miles Akim runs over the course of 18 days?

Answers

Hello!

First you have to list the miles he ran

He started with 1.75 and increases it by 0.25 miles every day

He ran 1.75, 2, 2.25, 2.5, 2.75, 3, 3.25, 3.5, 3.75, 4, 4.25, 4.5, 4.75, 5, 5.25, 5.5, 5.75 and 6 miles

Now we add all these numbers

1.75 + 2 + 2.25 + 2.5 + 2.75 + 3 + 3.25 + 3.5 + 3.75 + 4 + 4.25 + 4.5 + 4.75 + 5 + 5.25 + 5.5 + 5.75 + 6 = 69.75

The answer is B) 69.75 mi

Hope this helps!

On the 18th day, Akim runs 1.75 + 17×0.25 = 6 miles. Then his average mileage each day over the period is (1.75 +6)/2 = 3.875 miles.

Akim's total mileage is 18×3.875 = 69.75 miles. . . . . . . matches the 2nd choice

How do you solve this problem?

Answers

Very nice problem. You should look up the history of this question. It has a very long one having to do with mirrors made between 50 BC and 50 AD.

Step One
Find AB, BC, AC
Before beginning this problem, I'm going to arbitrarily name
c = AB
a = BC
b = AC It just makes the calculations easier.

AB = radius of the large circle - radius of the medium circle = 20.62 - 8.04 = 12.58
BC = Radii of the two smaller circles added together = 8.04 + 7.35 = 15.39
AC = Radius of the large circle - Radius of the small circle = 20.62 - 7.35 = 13.27

So
a = 15.39
b = 13.27
c = 12.58

Step Two
Find Angle A or <BAC
a^2 = b^2 + c^2 - 2*b*c * Cos(A)
15.39^2 = 12.58^2 + 13.27^2 - 2 * 12.58 * 13.27 * Cos(A)
236.852 = 158.26 + 176.1 - 333.87 * Cos(A)
236.852 = 334.4 - 333.87*Cos(A)
-97.55 = - 333.87 * Cos(A)
-97.55 / -333.87 = Cos(A)
0.2922 = cos(A)
A = cos-1(0.2922)
A = 73.01 degrees

Step Three
Just to see if you understand what was done, I'll give you the givens for finding c, and the answer and you can work through the calculations to see if your answer agrees with mine. If it doesn't PM me.
c = 12.58
b = 13.27
a = 15.39

12.58^2 = 13.27^2 + 15.39^2 - 2*13.27*15.39*Cos(C)
C = 51.42

Step Four
Find <B
Every triangle has 180 degrees so
B = 180 - <A - C
B = 180 - 51.42 - 74.01
B = <54.57.
I have found a moderator who opened the question up so that I can show you why the Cos law is the only way to do this. If the circles are very disproportionate as in this diagram, then no simple assumption can be made. The cos law is all that will work. I would have posted this earlier, but I didn't think anyone would find another method. It's ingenious but not possible for the situation below.

Other Questions

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