I need help please with these two questions.
1. What is the volume of this sphere? (First Picture)
8π cm³
16π cm³
27π cm³
36π cm³
2. What is the volume of this sphere? (Second Picture)
Use 3.14 for pi and round to the nearest hundredth when necessary.
615.44 cm³
2461.76 cm³
11,488.21 cm³
91,905.71 cm³
Answers
Answer:
(1) Volume of a sphere is [tex]36 \pi\ cm^{3}[/tex] .
(2)volume of the sphere is 11488.21 cm³ .
Step-by-step explanation:
Formula
[tex]Volume\ of\ a\ sphere = \frac{4}{3} \pi r^{3}[/tex]
Where r is the radius of the sphere .
Part First
As given the radius of the circle is 3cm .
Putting values in the formula
[tex]Volume\ of\ a\ sphere = \frac{4\times 3\times 3\times 3}{3} \pi[/tex]
[tex]Volume\ of\ a\ sphere = \frac{108}{3} \pi[/tex]
[tex]Volume\ of\ a\ sphere = 36 \pi\ cm^{3}[/tex]
Therefore the volume of a sphere is [tex]36 \pi\ cm^{3}[/tex] .
Second Part
As given
Diameter of the sphere is 28 cm .
[tex]Radius (r) = \frac{Diameter}{2}[/tex]
[tex]Radius (r) = \frac{28}{2}[/tex]
[tex]Radius (r) = 14\ cm[/tex]
[tex]\pi = 3.14[/tex]
Putting all the values in the formula
[tex]Volume\ of\ a\ sphere = \frac{4}{3}\times 3.14\times 14\times 14\times 14[/tex]
[tex]Volume\ of\ a\ sphere = \frac{4\times 3.14\times 14\times 14\times 14}{3}[/tex]
[tex]Volume\ of\ a\ sphere = \frac{34464.64}{3}[/tex]
[tex]Volume\ of\ a\ sphere =11488.21\ cm^{3}[/tex]
Therefore the volume of the sphere is 11488.21 cm³ .
1. The volume of the sphere is 16π cubic centimeters, which matches option B.
2. The correct answer for the volume of the second sphere is:
C. 11,488.21 [tex]cm^3[/tex]
1. For the sphere shown in the image with a diameter of 3 cm, the correct choice for its volume is:
B. 16π cm³
To calculate the volume of a sphere, we use the formula:
V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] r^3
Where r is the radius of the sphere.
Given:
- Diameter of the sphere = 3 cm
- Therefore, radius (r) = 3/2 = 1.5 cm
Substituting in the formula:
V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] (1.5)^3
V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] 3.375
V = 4 [tex]\times[/tex] π [tex]\times[/tex] 3.375/3
V = 16π cm³
So the volume of the sphere is 16π cubic centimeters, which matches option B.
2.For the second sphere shown with a diameter of 28 cm, to calculate its volume using π = 3.14 and rounding to the nearest hundredth, we follow these steps:
1) Find the radius by dividing the diameter by 2:
Radius = 28 cm / 2 = 14 cm
2) Use the formula for sphere volume: V = (4/3) [tex]\times[/tex] π [tex]\times[/tex] r^3
Substituting the values:
V = (4/3) [tex]\times[/tex] 3.14 [tex]\times[/tex] (14 cm)^3
V = (4/3) [tex]\times[/tex] 3.14 [tex]\times[/tex] 2744
V = 11,488.53 cm^3
3) Rounding to the nearest hundredth as instructed:
V = 11,488.53 cm^3 rounds to 11,488.21 cm^3
Therefore, the correct answer for the volume of the second sphere is:
C. 11,488.21 [tex]cm^3[/tex]
The correct question is:
1. What is the volume of this sphere? (First Picture)
A. 8π cm³
B. 16π cm³
C. 27π cm³
D. 36π cm³
2. What is the volume of this sphere? (Second Picture)
Use 3.14 for pi and round to the nearest hundredth when necessary.
A. 615.44 cm³
B. 2461.76 cm³
C. 11,488.21 cm³
D. 91,905.71 cm³
Related Questions
100 points? Yea, that's right!
Question 3 options: (be sure to explain)
A.) a scalene hexagon -- i know it is not true
B.) a regular hexagon -- not sure
C.)an equiangular hexagon -- my best guess.
D.) an equilateral hexagon -- i know it is not true
Answers
Number 2
a rectangle has congruent diagonals because if you draw them out, the parallelogram has one diagonal that is long and one that is shorttrapezoids dont necessarily have congruent diagonalsrectangles have to have congruent diagonals
Hello!
The most logical answer would be a quiangular hexagon
I hope it helps!
Hassan built a fence around a square yard. It took 500 feet of lumber to build the fence. The fence is 5 feet tall. What is the area of the yard inside the fence?
Answers
The area of the yard inside the fence will be 15,625 feet². Square centimeters and other similar units are used to measure area.
What is the area?The space filled by a flat form or the surface of an item is known as the area.
lumber required to build the fence = 500 feet
The side of the square yard is ;
[tex]\rm a = \frac{500}{4} \\\\ a =125\ feet[/tex]
The fence is 5 feet tall. The area of the yard inside the fence is found as;
[tex]\rm A_f = side \times side \\\\ \rm A_f =125 \times 125 \\\\ \rm A_f =15,625 \ feet^2[/tex]
Hence the area of the yard inside the fence will be 15,625 feet².
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The equation shown below involves a perfect square trinomial.
9x2 - 24x + 16 = 11
Which of the following is a step in solving this equation?
A. Divide both sides by 8
B. Subtract 16 from both sides
C. Square both sides
D. Take the square root of both sides
Answers
Which type of line establishes special angle relationships when intersected with one or more lines?
Answers
There are two types of lines: perpendicular and parallel lines; parallel lines have same position and same length but do not touch each other or one another. While perpendicular lines may or may not have the same size but intersects with each other. The resulting intersections for angles.
Please help me with this question....
Is 0.17 repeating times square root of 108 rational or irrational? Justify your answer.
Answers
Any repeating number is rational.
The square root of 108 is 10. 3923048454
It is irrational. Its numbers do not repeat.
So, if you were to multiply a rational and irrational number, it would be irrational.
We can even test this:
.17171717171717171717171*10.392304....= 1.784537....
I hope this helps!
~kaiker
Due to his good credit history, Francis was able to purchase a home with a good interest rate on his loan. Assuming Francis has the ability to choose the length of his loan and the amount of the down payment, what method would help Francis decrease the total cost of the loan? Select the best answer from the choices provided. reducing the down payment increasing the length of the loan increasing the length of the loan and reducing the down payment reducing the length of the loan and increasing the down payment
Answers
Reducing the length of the loan and increasing the down payment.
Explanation:
Increasing the down payment will reduce the total amount you will owe to the bank so there will be less interest charges.
The smaller the term, the higher the interest rate but the smaller the time the less the bank will actually receive from you.
Answer:
Reducing the length of the loan and increasing the down payment
Step-by-step explanation:
Assuming Francis has the ability to choose the length of his loan and the amount of the down payment.
The method that would help Francis to decrease the total cost of the loan is - reducing the length of the loan and increasing the down payment.
When a person pays more amount in down payment, then he will have to loan out a smaller amount. And he will have to pay less interest. If the loan is short, the interest to be paid will be less. If the loan term is long, the interest also increases. One has to pay interest for the whole tenure of the loan.
So, if someone wants to reduce the loan amount, he must pay more in down payment.
-(5)^-1
-1/5
-5
5
1/5
Answers
= −1/5
Answer = −1/5 (A)
a pizzeria sells a round pizza with the diameter of 24 inches. what is the area and what is the circumferance
Answers
Area=pi*r²
D=24 in------------ > r=D/2=24/2=12 in
Area =pi*12²=452.16 in²
the circumference=2*pi*r=2*pi*12=75.36 in
the answer is
the area is 452.16 in² and the circumference is 75.36 in
Cool Scoops ice cream shop offers 42 different one-topping sundaes. If there are 7 flavors of ice cream, how many toppings are there?
a.6
b.5
c.3
Answers
42/7=6
Hope this helps☺
Answer:
A
Step-by-step explanation:
The correct answer is A. 6
How many ways are there to distribute five balls into seven boxes if?
Answers
1. 1,2,3,4,5 - 1,2,4,5,3 - 1,4,5,3,2...... So on Hope this helps:)
A photo processing place can develop 488 photos in 8 hours. How many photos can it develop every hour? A. 61 photos B. 480 photos C. 496 photos D. 3,904 photos
Answers
So l, it can develop (answer A) 61 photos every hour.
x= # photos in 1 hour
488/8 = x/1
cross multiply
(488*1)= (8*x)
488=8x
divide by 8
61= x
They can process A) 61 photos in one hour.
Hope this helps! :)
What is the equation of the line in slope-intercept form that is perpendicular to the line y =
3/4x – 2 and passes through the point (–12, 10)? y = x – 6 y = x + 6 y = x + 26 y = x + 10
Answers
Which is an equivalent expression for 14+10x+6−8x?14+10x+6−8x?
Answers
= 2x +20
If 2a+3b=12 and ab=6 find the value of 8a^3+27b^3
Answers
B) ab = 6 solving for a
B) a = 6 / b then we substitute this into equation A)
A) 12 / b + 3b = 12 multiplying this by "b"
A) 12 + 3b^2 = 12b
A) 3b^2 -12b +12= 0 dividing by "3"
A) b^2 -4b + 4 = 0
Factoring
(b-2) * (b-2) = 0
b = 2
Since b = 2 then a = 3
NOW, we put these numbers into:
8a^3 +27b^3
8*3*3*3 + 27*2*2*2
216 + 216
The answer is 512
a = 6/b
2 *6/b + 3b = 12
12/b + 3b = 12
12 + 3b^2 = 12b
3b^2 - 12b + 12 = 0
b^2 - 4b +4 = 0
(b - 2)^2 = 0
b = 2
a will = 3
8*3^3 + 27*2^3
8*27 + 27*8
I'm getting 432
I thought perhaps I could do this a shorter way. Turns out I can't. If you give out a Brainly Please give it to the other responder.
What are the solutions to the equation x² = 256?
Answers
x = - 16
You could do it this way
x^2 - 256 = 0
(x - 16)(x + 16) = 0
x - 16 = 0
x = 16
x + 16 = 0
x = - 16
x = ±√256
x = ±16
the solutions are x = -16 and x = 16
Why does a negative number times a negative number equal a positive number?
Answers
b(t)=50(1.4)^t
What is the y-intercept of the function?
What does this mean in the context of the problem?
Answers
What is the y-intercept of the function?
The intersection with the y-axis of the function you find when x = 0.
In this case we have:
For t = 0:
B (0) = 50 (1.4) ^ 0
B (0) = 50 * (1)
B (0) = 50
Answer:
the y-intercept of the function is:
B (0) = 50
What does this mean in the context of the problem?
You must place the complete statement to answer exactly.
However, in any problem of exponential type, it means the initial quantity of something.
If we refer to the increase in population over time, then the intersection with the y-axis is the initial population.
simplify 6a^(2)-[-5-(9a^(2)-3a)]-[8+(-19a-8)]
Answers
Graph the solution for the following system of inequalities. Click on the graph until the correct solution is displayed. 2x + y < 0 y ≥ -4 - 2x
Answers
The graph for these inequalities intersects at point (0,0).
The graph displays the solution to the system of inequalities: 2x + y < 0 and y ≥ -4 - 2x. Here's a breakdown:
First Inequality (2x + y < 0):
This translates to a blue line with a negative slope. Points like (0, -2) and (3, -6) lie on this line.
We shade the region below this line because the inequality specifies "less than." Points there, like (1, -5), satisfy the inequality.
Second Inequality (y ≥ -4 - 2x):
This translates to a green line with a negative slope as well. Points like (0, -4) and (2, -8) lie on the line.
Unlike the first, we shade the region above this line because the inequality specifies "greater than or equal to." Points like (1, -3), above the line, satisfy the inequality.
Combined Solution:
The solution space is the overlap where both inequalities hold true. This is the triangular region shaded in both blue and green. Points within this region, like (1, -5), satisfy both inequalities.
Checking Points:
If unsure about shading, test points outside the shaded region. For example, point (0, 0) lies above both lines, satisfying both inequalities. This confirms the shading is correct.
The circumference of a circle is 40π. Find the diameter.
Answers
a)Natalie has read 3/4 of a book that is 120 pages long. How many pages does she have left to read?
b) What is: one half of 45?
c) What is: one third of 50?
d) What is one half of 1/4 ?
e) what is one third of 73
f) What is: one third of 1/3 ?
g) what is one third of 1/9?
Please help! I think I know but somehow, my answers are all wrong. 20 points
Answers
B) 22.5 or 22 1/2
C)1/3*50=16.67
D)0.125
E)1/3*70=24.33
F)1/9
G)0.37
Answer:
a) 30 pages b) 22.5 or 45/2 c)50/3 or 16.67 d) 1/8 e) 73/3 or 24.33 f)1/9 g) 1/27
Step-by-step explanation:
a) If Natalie has read 3/4 then all that's left is 1/4 of the book to read a whole book since 3/4+1/4=4/4=1
1/4 of 120=30 pages
b) One half of 45 is the same as dividing it by two or multiplying by 1/2.
1/2*45=45/2 =22.5
c) One third of 50, is the same of multplying by 1/3 then 1/3*50≈16.67
d) Take a look back at letter b. One half (1/2) of 1/4 is :
[tex]\frac{1}{2}*\frac{1}{4}=\frac{1}{8}[/tex]
e) One third of something, is 1/3 times something like previous cases above so 1/3*73=73/3≈24.33
f) One third of One third, is 1/3 times 1/3:
[tex]\frac{1}{3}*\frac{1}{3}=\frac{1}{9}[/tex]
g) One third of 1/9 is 1/3 times 1/9:
[tex]\frac{1}{3}*\frac{1}{9}=\frac{1}{27}[/tex]
Do not forget the rules of multiplying fractions. Numerator times Numerator, Denominator times Denominator. When we read a third, half,.. of this means one half times
How can one 1/4x − 3 = 1/2x + 8 be set up as a system of equations?
a. 4y + 4x = −12
2y + 2x = 16
b.4y − x = −12
2y − x = 16
c.4y + x = −12
2y + x = 16
d.4y − 4x = −12
2y − 2x = 16
Answers
Left side:
.. y = 1/4x -3
.. 4y = x -12 . . . . multiply by 4
.. 4y -x = -12 . . . subtract x
Right side:
.. y = 1/2x +8
.. 2y = x +16 . . . multiply by 2
.. 2y -x = 16 . . . subtract x
These equations correspond to selection B.
Is triangle ABC similar to triangle ADE? Justify your answer.
Answers
No! Triangle ABC is not similar to triangle ADE.
Triangle ABC is not similar to triangle ADE because the sides of triangle ADE is not corresponding to that of Triangle ABC.
Similar triangles are triangles that share the same shape but may differ in size. This means that while their corresponding angles are equal, their corresponding sides are proportional.
For two triangles to be considered similar:
Their corresponding angles must be congruent (equal).Their corresponding sides must be in proportion.In practical terms, this means that if you were to resize one triangle while maintaining the same angle measurements, you could transform it into the other triangle. The concept of similarity plays a crucial role in various mathematical fields, including geometry, trigonometry, and calculus. It enables us to solve problems involving indirect measurements, scale drawings, and geometric relationships.
Fifty people are surveyed at a state fair. Of the 50 people, 30 like funnel cake and 25 like fried oreos. Twenty people like both funnel cakes and fried oreos. Use a Venn Diagram to organize the data and answer the questions. How many people like either funnel cake or fried oreos?
Answers
55
When using a Venn diagram to determine how many people like either funnel cake or fried Oreos out of a survey of 50, after subtracting the 20-person overlap from each individual preference to avoid double counting, the total number liking either is found to be 35 people.
To determine how many people like either funnel cake or fried Oreos, we need to use the concept of set union from Venn diagrams. First, we draw two overlapping circles, one for people who like funnel cake and another for those who like fried Oreos.
The overlapping area represents people who like both. Given that 30 people like funnel cake and 25 like fried Oreos, with a 20-person overlap liking both, we add the individual preferences and subtract the overlap to avoid double counting.
The representation is:
Number liking funnel cake only: 30 - 20 = 10
Number liking fried Oreos only: 25 - 20 = 5
Number liking both: 20
Adding these, the total number liking either funnel cake or fried Oreos is 10 + 5 + 20 = 35 people.
17 POINTS. Find the x and y intercepts and show work please.
It’s number 2. y=x^4+2x^2-1
Answers
The first think I always do in such a question is get the graph.
Go to wolfranalpha.com and see the graph to tell me what I'm looking for.
Put y = x^4 + 2x^2 - 1 into the input bar. You find out that there are only 2 answers.
Use the Quadratic Formula
a = 1
b = 2
c = - 1
Then let z = x^2
So the new equation is
y = z^2 + 2x - 1
You solve for z and you get
z1 = 0.4142 and z2 = - 2.4142 You can go no further with z2 because the square root of a minus number can't be graphed on the coordinate system.
z = x^2
0.4142 = x^2
x = +/- 0.6435
Note to moderator
When I send a student to wolframalpha, the work is mine and I'm not copying and pasting anything that isn't allowed by wolfram
What is the explicit rule for the sequence?
47,42,37,32, …
an=42−5n
an=5n+42
an=5n+52
an=52−5n
Answers
General Idea:
Arithmetic sequence is a sequence which have common difference. The [tex] n^{th} [/tex] term of arithmetic sequence is given by the below formula:
[tex] a_n=a_1+(n-1)\cdot d\\ \\ Where:\\ a_1 \; is \; the \; first\; term\; of\; the\; sequence\\ n is \; the\; number \; of\; terms\; in\; the\; sequence\\ d\; is\; the\; common\; difference\; =\; a_2-a_1 [/tex]
Applying the concept:
47,42,37,32, …
[tex] a_1=47\\ \\ a_2=42\\ \\ d=a_2-a_1=42-47=-5\\ \\ a_n=47+(n-1) \cdot -5\\ a_n=47-5(n-1)\\ Distributing \; 5\; inside \; the \; parenthesis\\ \\ a_n=47-5n+5\\ Combine\; like\; terms\\ \\ a_n=52-5n [/tex]
Conclusion:
The explicit rule for the sequence 47,42,37,32 is [tex] a_n=52-5n [/tex]
suppose a classmate claims that the differnece between (x+2)2 and (x2+4) mist be 0. Is your classmate correct? Choose the best explanation.
Answers
No, the classmate is not correct. The difference between (x+2)² and (x²+4) is 4x.
Explanation:No, your classmate is not correct. The difference between (x+2)² and (x²+4) is not necessarily 0. To find the difference, we need to expand both expressions and then simplify:
(x+2)² = x² + 4x + 4
(x²+4) = x² + 4
So, the difference between the two expressions is (x² + 4x + 4) - (x² + 4) = 4x. Hence, the difference is not 0.
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Suppose a - b = 0.
Which one of these expressions equals ab?
a. a^2
b. 0
c. 2b
d. 2a
e. a/b
Answers
a-b=0-----------------> a=b
b=a
therefore
a.b--------> substituting---------> a*(a)=a² or b*b=b²
the answer is the option A) a²
Which measurement is most accurate to describe the width of a math book?
8 inches
2 feet
1 yard
2 inches
Answers
Darlene's Caillou's 8 gallons of gasoline to travel 340 miles at mechanic work on the car and use 7 gallons of gasoline to travel 350 miles if the price of gasoline was approximately $4 per gallon how much less to the nearest cent per get a smile that it cost to run after the mechanic work on it
Answers
340 miles with 8 gallons.
A gallon costs $4, so 8 gallons cost 8 * $4 = $32.
$32 per 340 miles = $32/340 = $0.0941/mile = 9.4 cents/mile
After mechanic:
350 miles with 7 gallons.
7 gallons cost 7 * $4 = $28.
$28 per 350 miles = $28/350 = $0.08/mile = 8 cents/mile
The difference is 9.4 - 8 = 1.4.
To the nearest cent, round 1.4 to 1.
Answer: After the mechanic, it cost 1 cent per mile less to run the car.