There are 4 different flower boxes with different-size bases that can hold exactly 16 cubic feet of soil when using whole-number dimensions. These consist of dimension combinations of 1x1x16, 1x2x8, 1x4x4, and 2x2x4 feet.
Mrs. Wilton is planning a rectangular flower box that should have a volume of 16 cubic feet. To find how many flower boxes with different-size bases can hold exactly 16 cubic feet of soil, we need to find all the possible combinations of whole-number dimensions (length, width, and height) that when multiplied together equal 16 cubic feet. We must remember that volume is calculated as Length x Width x Height. Since 16 is the volume in cubic feet, we look for whole-number factors of 16.
Here are the possible whole-number dimension sets (in feet) for a volume of 16 cubic feet:
1 x 1 x 16 (Height can be 1, 16, or any factor of 16)
1 x 2 x 8 (Height can be 2, 8, or any factor of 16)
1 x 4 x 4 (Height can be 4 or any factor of 16)
2 x 2 x 4 (These dimensions are interchangeable)
Each of these dimensions gives a different base size for the flower box, and all ensure the volume is 16 cubic feet. Thus, there are 4 different flower boxes with different-size bases that will hold exactly 16 cubic feet of soil.
can someone please help !!!
Answer:
s=-8
Step-by-step explanation:
Can 4 cm, 7 cm, 9 cm be a right triangle
Answer:
No
Step-by-step explanation:
For it to be a triangle c² = a² + b²
The longest side is c (9)
and 81 ≠ 49 + 16
Can I get brainliest
Answer:
No
Step-by-step explanation:
Since it might be a right triangle, we can test the values using the Pythagorean theorem.
[tex]a^2+b^2=c^2[/tex]
a and b are the legs, and c is the hypotenuse.
We know that 4 and 7 are the legs, or a and b. This is because they are two smaller sides. We know that 9 is the hypotenuse, or c. This is because it is the longest side.
[tex]4^2+7^2=8^2[/tex]
Solve the exponents
[tex]16+49=81[/tex]
65=81
[tex]65 \neq 81[/tex]
Since 65 does not equal 81, this cannot be a right triangle
What is circumference? Please select all that apply:
A) distance around the circle
B) the space inside the circle
C) To find the circumference C of a circle if you know the diameter d is to multiply pi by the diameter
D) To find the circumference if you know the radius, replace d with 2r in the formula
E) the formula for circumference is C=pi + r
Answer:
A, C and D are correct.
\
Step-by-step explanation:
A is correct.
B is false; that space is the "area" of the circle.
C is true. C = πd
D is true. C = 2πr
E is false. Way off.
Final answer:
Circumference is the distance around a circle, calculated as C = πd or C = 2πr, depending on whether the diameter or radius is known. (Option A,C,D)
Explanation:
Circumference is the term used to describe the distance around a circle. When calculating the circumference, you can use different formulas depending on the information you have about the circle. If you know the diameter (d), the circumference (C) can be found by multiplying the diameter by pi (π), using the formula C = πd. Alternatively, if you know the radius (r) of the circle, you can use the formula C = 2πr since the diameter is twice the radius (d = 2r).
The correct answers to the question are:
A) distance around the circleC) To find the circumference C of a circle if you know the diameter d is to multiply pi by the diameterD) To find the circumference if you know the radius, replace d with 2r in the formulaIt's important to note that the space inside the circle is referred to as the area, not the circumference, and the formula for circumference is not C = pi + r as stated in option E, but rather C = πd or C = 2πr.
jazzy...respond pls..A box contains different-colored marbles that are all the same size. The table below shows the colors and amount of each marble in the box:
Color of Marble Number
Red 4
Blue 8
Green 3
Pink 5
Allen selects a marble from the box randomly, without looking, and then tosses a fair coin. What is the probability that Allen will select a red marble and the coin will land heads up?
Answer:
well is a 50 50 chains that Allen will get a red marble and
a 50 50 that the coin will land heads up.
Step-by-step explanation:
What is the rate of the interest on $560 for two years is $145.60?
The rate of interest is 13%.
Step-by-step explanation:
Given,
Principal (P) = $560
Interest (I) = $145.60
Time (T) = 2 years
To find the rate of interest
Formula
If P principal was invested for T years at r% simple interest, the interest will be I = [tex]\frac{PTr}{100}[/tex]
So,
Putting the values of P, I, T we get,
145.60 = [tex]\frac{560X2Xr}{100}[/tex]
or, r = [tex]\frac{145.60X100}{2X560}[/tex]
or, r = 13%
Hence,
The rate of interest is 13%.
Which of the following equations was used to graph the line shown?
Graph where both the axes run from minus sux to plus six and beyond. Straight lines intersect the aves at (6, 0) and (0, 6)
A. y = 6 + x
B. y = 6 – x
C. y = x – 6
D. y = 6x
The answer would be D since it forms a straight line along the x-axis
How many different combinations of 3 books can Erika take on a trip if she has 5 books
Answer:
10 combinations
Step-by-step explanation:
What we have to do is calculate the number of combinations of 3 in 5.
The formula for the combinations is:
nCr = n!/r!(n-r)!
in this case n = 5 and r = 3
replacing
5C3 = 5!/3!(5-3)! = 5!/(3!*2!)
5C3 = 10
So there are 10 combinations in which Erika can enjoy the books on her trip
Answer:
The number of different combinations of 3 books that Erika can take on a trip if she has 5 books is 10
Step-by-step explanation:
Here we have the formula for combination given as follows;
[tex]\binom{n}{r} = \frac{n!}{r!(n-r)!}[/tex]
Where n is the number of set elements = 5 and
r = Number of subset elements = 3
Therefore, plugging the values, we have;
[tex]\binom{5}{3} = \frac{5!}{3!(5-3)!} = \frac{120}{6(2)} = 10[/tex]
Therefore, the number of different combinations of 3 books that Erika can take on a trip if she has 5 books = 10.
Match each mathematical expression with its simplified form.
(2 +9+4)
(3 + 1 + 4 + 8)
Answer:
15 and 16
Step-by-step explanation: To get simplified form, you add the numbers in parentheses together. (2+9+4)= 15 and (3+1+4+8)=16
For problem 1. 2+9=11 11+4=15
For problem 2. 3+1=4 4+4=8 8+8=16
Hopefully this helped, and please add me as brainliest.
Final answer:
The simplified forms of the expressions (2 + 9 + 4) and (3 + 1 + 4 + 8) are 15 and 16, respectively. The placement of parentheses affects the outcome of mathematical operations significantly, and careful evaluation following the order of operations is essential for accurate simplification, particularly when nested expressions are involved.
Explanation:
The question requires matching each mathematical expression with its simplified form. Let's simplify the given expressions:
(2 + 9 + 4) simplifies to 2 + 9 + 4 = 15.
(3 + 1 + 4 + 8) simplifies to 3 + 1 + 4 + 8 = 16.
Now, to address your example concerning the importance of the placement of parentheses, consider the expression 2 + (3 x 5). If the parentheses are around (2 + 3), the result is different than if the parentheses are around (3 x 5). Without any parentheses, the order of operations dictates that multiplication is done before addition. Hence:
(2 + 3) x 5 = 5 x 5 = 25 (since addition within parentheses is done first, followed by multiplication).
2 + (3 x 5) = 2 + 15 = 17 (since multiplication within parentheses is done first, followed by addition).
From an airplane at an altitude of 1400 meters, the angle of depression to a rock on the ground measures 31°. Find the direct line distance from the plane to the rock. Round to the nearest tenth of a meter.
Answer:
1633.3 meters
Step-by-step explanation:
-Given the angle of depression is 31°, and the plane's height above the ground is 1400m.
-We use the Law of Sines to determine the distance between the plane and the rock.
-The angle of elevation from the rock to the plane is(corresponds to the plane's altitude):
[tex]\angle elevation=90-31\\=51\textdegree[/tex]
#Now, using Sine Law;
[tex]\frac{a}{Sin \A}=\frac{b}{Sin \ B}\\\\\\\frac{1400}{Sin \ 59}=\frac{d}{Sin \ 90}\\\\\\\\=1633.287\approx 1633.3\ m[/tex]
Hence, the direct distance between the plane and the rock is 1633.3 meters
The university is on a bearing of 050 degrees from the stadium and 300 degrees from the hospital. Mark the position of the university on the map with a cross
The position of the university marked x is shown in the attachment.
Given that university is on a bearing of 050 degrees from the stadium and 300 degrees from the hospital.
so we can say that the university position is gotten relative to the the position of the stadium and hospital.
The university is 50° from the stadium and then 350° from the hospital.
I.e it is N 50° E from the stadium and N 60° W from hospital.
The angle forms will be 50+60 = 110°
The point where the two lines intersect is the position of the university. Mark this point with a cross on the map.
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In a computer catalog, a computer monitor is listed as being 27 inches. This distance is
the diagonal distance across the screen. If the screen measures 15 inches in height, what
is the actual width of the screen to the nearest inch?
The width of the computer monitor is 22 inches
What is a Rectangle?
In a Rectangle
It is a four sided shape where every angle is a right angleThe alternative sides are equalTwo axes of symmetry bisect each otherDiagonals are equal in lengthThe diagonal equals the square root of the width squared plus the height squared
Given data ,
Let the Width of the rectangle be W
Diagonal of the rectangle = 27 inches
Height of the rectangle = 15 inches
D² = L² + W²
W² = D² - L²
W² = ( 27 )² - ( 15 )²
= 729 - 225
= 504
Therefore , Width W = √504
≈ 22.45 inches
≈ 22 inches
Hence , the width of the computer monitor is 22 inches
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If you double president Reagans age at the time of his first inauguration and subtract his age at the time he died,the result is 45 years. How old was president Reagan when he died?
Answer:
93
Step-by-step explanation:
Let's say President Reagan was x years old when he died. He was 69 years old at his first inauguration
(2*69)-x = 45
Wait. But how will we find x in that equation?
--> (2*69)-45 = x
That's better.
2*69 = 138
138-45 = 93
x=93
what is 4p−5(p+6) simplified
Answer:
-p - 30
Step-by-step explanation:
4p−5(p+6)
Distribute:
=4p+(−5)(p)+(−5)(6)
=4p+−5p+−30
Combine Like Terms
=4p+−5p+−30
=(4p+−5p)+(−30)
=−p+−30
=−p−30
If the campers at Camp Grilled Meat prefer hot dogs to hamburgers by a ratio of 4:3, and they need 500 hot dogs, how many hamburgers will they need?
Answer:
375
Step-by-step explanation:500 equals 100% divide by 4 its 125 times 3 equals 375, your welcome
Answer:
They will need 375 hamburgers.
Step-by-step explanation:
Keeping the ratio in mind, we solve this problem by cross multiplying. Set up the ratio 4/3 and set it equal to the greater ratio of 500/(an unknown number of hamburgers, represented by x). Cross multiply to end up with the equation 4x=1500. (Cross multiplying is multiplying each numerator by the opposite denominator). Solve for x in the above equation using SADMEG. You divide 1500 by 4 and end up with 375 hamburgers.
Suppose you drop a ball from a height of 10 feet. After the ball hits the floor, it rebounds to a height defined by the recursive formula an = 0.85an – 1. What is a1?
Answer:
10 feet
Step-by-step explanation:
The height of the ball after it hits the floor and rebound is defined by the recursive formula:
[tex]a_n = 0.85a_{n-1}[/tex]
This is an example of a geometric sequence in which the next term is gotten by multiplication of the previous term by 0.85.
If the ball is dropped from a height of 10 feet, the first term is 10.
Its Initial height, [tex]a_1=10 \:feet[/tex]
Sharon has 72 beads. She has twice as many sphere beads as cylinder beads. How many of each kind of bead does Sharon have? How did you solve the problem? How can you check your check.
Answer:
Sphere=48 beads
Cylinder=24 beads
Step-by-step explanation:
Let the number of cylinder beads be y and since she has twice as many sphere beads, the sphere beads will be 2y
The sum of sphere and cylinder beads will be y+2y=3y
This sum is equivalent to the total number given as 72
Therefore, equating 3y to be equal to 72 we obtain the equation
3y=72
Dividing by 3 on both sides we obtain that
Y=72/3=24 beads for cylinder
Since the sphere is 2y then 2*24=48
To confirm, it is evident that 48+24=72
Also, the number 48 is double/twice the number 24
What single decimal multiplier would you use to increase by 7% followed by a 9% increase?
Answer:
The decimal multiplier is 1.1663
Step-by-step explanation:
Since the increases are done successively we can find decimal numbers for each one and multiply both to have a single decimal representing the whole operation. When there's a increase this means that we have the original value (100%) summed by some other value, in this case 7%, so the new value would be 100% + 7% = 107%, we can transform this to a decimal number by dividing it by 100, so 107/100 = 1.07. The same applies to the 9% increase, so we would have 109/100 = 1.09. We can now multiply both to obtain a single decimal multiplier, we have:
1.07*1.09 = 1.1663
Having trouble with this problem. Please help
Answer:
A) 33 3/4°
Step-by-step explanation:
The supplement of an angle is the difference between 180° and the angle measure:
supplement of 146 1/4° = 180° -(146 1/4)°
= (180° -146°) -1/4° = 34° -1/4°
= 33 3/4° . . . . supplement of the given angle
1 4/9 + 2 6/9 is equal to 4 1/9, true or false?
Answer: True
Explanation: To add mixed numbers, first add the fractions.
So here, we have 4/9 + 6/9 which is 10/9.
Then add the whole numbers.
So we have 1 + 2 which is 3.
So our answer is 3 and 10/9.
But notice, that since 10/9 is an improper fraction,
our answer is not in lowest terms.
10/9 can be rewritten as the mixed number 1 and 1/9.
So 3 and 10/9 is the same as 3 + 1 and 1/9 which is 4 and 1/9.
Since 4 and 1/9 is in lowest terms, this is our final answer.
So we can say that 1 and 4/9 + 2 and 6/9 is 4 and 1/9.
△BCD is a right triangle. The length of the hypotenuse is 18 centimeters. The length of one of the legs is 14 centimeters. What is the length of the other leg?
Answer:
The answer to your question is b = 11.31 cm or 8[tex]\sqrt{2}[/tex] cm
Step-by-step explanation:
Data
hypotenuse = 18 cm
one leg = 14 cm
second leg = ?
Process
1.- Use the Pythagorean Theorem to solve this problem
c² = a² + b²
c = hypotenuse
a = longer leg
b= shorter leg
2.- Substitution
18² = 14² + b²
-Solve for b
b² = 18² - 14²
-Simplify
b² = 324 - 196
b² = 128
-Find the prime factors of 128
128 2
64 2
32 2
16 2
8 2
4 2
2 2
1
128 = 2⁶2¹
-Result
b = 11.31 or 8[tex]\sqrt{2}[/tex]
Answer:
21.32 Cm
Step-by-step explanation:
Add up the centiminer
Help me! 17 points to help me
Answer:
this is to much work for me to do.
Step-by-step explanation:
A coin is flipped and a normal dice is rolled.
a)
How many possible outcomes are there?
b)
What is the probability of getting a tail and a five?
c)
What is the probability of getting a number less than five and a head?
Total possible outcomes if a coin is flipped and a normal dice is rolled are 12
Probability of getting a tail and a five will be 1/12
The probability of getting a number less than five and a head is 1/3
What is probability?Probability is the chance of happening of an event.Probability is always ≤ 1How to find out how many possible outcomes are there?If a coin is tossed 2 possible outcomes will be there. Either it will be a Head or a Tail.If a normal dice is rolled 6 possible outcomes will be there.∴ Total possible outcomes = (6 x 2) = 12
How to know the probability of getting a tail and a five?As we know that there will be 12 possible outcomes .Getting a five and a tail will be one of those possible outcomes.∴ Probability of getting a tail and a five will be 1/12
How to know the probability of getting a number less than five and a head?We know that probability of getting a head when a coin is flipped is 1/2 Probability of getting a number less than five is a dice is rolled is = 4/6∴ The probability of getting a number less than five and a head = (1/2)(4/6) = 4/12 = 1/3
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A teacher allows her students to decide whether to use the mean, median, or mode to determine their test averages. One student determined that he will receive the highest average if he uses the mean. Which test scores are his?
A. 95, 82, 76, 95, 96B. 79, 80, 91, 83, 80C. 65, 84, 75, 74, 65D. 100, 87, 94, 94, 81
Final answer:
Option D, with scores of 100, 87, 94, 94, and 81, yields the highest average when calculated using the mean, making it the best choice for the student seeking the highest test average.
Explanation:
The question asks which set of test scores will give the highest average if calculated using the mean. To find the answer, we calculate the mean of each set of scores:
A: (95+82+76+95+96)/5 = 88.8
B: (79+80+91+83+80)/5 = 82.6
C: (65+84+75+74+65)/5 = 72.6
D: (100+87+94+94+81)/5 = 91.2
Among the options, option D has the highest mean.
Therefore, the student with test scores of 100, 87, 94, 94, and 81 will have the highest average when using the mean to calculate.
Two sides of a triangle measure 8 cm and 15 cm. Which could be the length of the third side?
6 cm
18 cm
24 cm
28 cm
Answer:
Option 2 is correct
Since only 18 is less than 23 and greater than 7, therefore the possible length of third sides is 18 cm and option 2 is correct.
What is the value of cosθ given that (−2, −3) is a point on the terminal side of θ ?
Answer:
-0.555
Step-by-step explanation:
The terminal point of the vector in this problem is
(-2,-3)
So, it is in the 3rd quadrant.
We want to find the angle [tex]\theta[/tex] that gives the direction of this vector.
We can write the components of the vector along the x- and y- direction as:
[tex]v_x = -2\\v_y = -3[/tex]
The tangent of the angle will be equal to the ratio between the y-component and the x-component, so:
[tex]tan \theta = \frac{v_y}{v_x}=\frac{-3}{-2}=1.5\\\theta=tan^{-1}(1.5)=56.3^{\circ}[/tex]
However, since we are in the 3rd quadrant, the actual angle is:
[tex]\theta=180^{\circ} + 56.3^{\circ} = 236.3^{\circ}[/tex]
So now we can find the cosine of the angle, which will be negative:
[tex]cos \theta = cos(236.3^{\circ})=-0.555[/tex]
Which type(s) of equation can have infinite solutions?
A. linear-linear
B. linear-quadratic
C. quadratic-quadratic
Answer:
A and C
Step-by-step explanation:
I did the assignment
A data set includes 103 body temperatures of healthy adult humans having a mean of 98.9degreesf and a standard deviation of 0.67degreesf. construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. what does the sample suggest about the use of 98.6 degreesf as the mean body temperature?
A 99% confidence interval for the mean body temperature can be calculated using the sample mean, standard deviation, and the t-score corresponding to the confidence level. The findings may suggest that the commonly accepted average body temperature of 98.6°F could be reconsidered if it does not fall within this interval.
Constructing a 99% Confidence Interval
To construct a 99% confidence interval for the mean body temperature of all healthy humans, we use the sample mean, standard deviation, and the t-distribution since the population standard deviation is not known. With a mean of 98.9°F, a standard deviation of 0.67°F, and a sample size of 103, we can calculate the margin of error using a t-score that corresponds to the 99% confidence level.
First, we find the t-score from the t-distribution table for 102 degrees of freedom (n-1) that corresponds to a 99% confidence level. Then, we calculate the margin of error using the formula:
Margin of Error (E) = t-score * (standard deviation / sqrt(n))
This margin of error is then added and subtracted from the sample mean to obtain the confidence interval:
Lower Limit = Mean - Margin of Error
Upper Limit = Mean + Margin of Error
This confidence interval provides a range within which we can be 99% confident that the true mean body temperature of all healthy humans lies.
Implications for 98.6°F as Average Body Temperature
The sample suggests that the mean body temperature of 98.6°F might not be accurate for all individuals. If the constructed 99% confidence interval does not contain the traditional mean of 98.6°F, it could indicate that the average body temperature is different than what has been historically taught.
The 99% confidence interval estimate of the mean body temperature of all healthy humans is approximately (98.7294, 99.0706) degrees Fahrenheit.
To construct a 99% confidence interval for the mean body temperature of all healthy humans, we'll use the formula:
[tex]\[ \text{Confidence Interval} = \bar{x} \pm z \left( \frac{s}{\sqrt{n}} \right) \][/tex]
Let's calculate the confidence interval:
[tex]\[ \text{Confidence Interval} = 98.9 \pm 2.576 \left( \frac{0.67}{\sqrt{103}} \right) \]First, let's calculate \(\frac{s}{\sqrt{n}}\):\[ \frac{s}{\sqrt{n}} = \frac{0.67}{\sqrt{103}} \approx 0.0662 \][/tex]
Now, we can find the margin of error:
[tex]\[ \text{Margin of Error} = 2.576 \times 0.0662 \approx 0.1706 \]Finally, construct the confidence interval:\[ \text{Confidence Interval} = 98.9 \pm 0.1706 \][/tex]
So, the 99% confidence interval estimate of the mean body temperature of all healthy humans is approximately (98.7294, 99.0706) degrees Fahrenheit.
.If a golf ball has a diameter of 4.3 centimeters and a tennis ball has a diameter of 6.9 centimeters. Find the difference between the volumes of the two balls.
Answer:
130.43 cm³
Step-by-step explanation:
To find the difference between the volumes of the balls, we must first find the volumes of the balls. To find the volume of each ball, we must first determine their shape. We understand that both balls are spherical.
The volume V of a sphere wit radius r is given as
V = 4/3 πr³
where r is the result when the diameter of the sphere is divided by 2.
Hence the radius of the Golf ball
= 4.3cm/2
= 2.15cm
radius of the tennis ball
= 6.9cm/2
= 3.45cm
The difference between the volumes of the two balls
= 4/3 π (3.45³ - 2.15³)
= 130.43 cm³
Harry Potter is at Ollivanders Wand Shop. As we all know, the wand must choose the wizard, so Harry cannot make the choice himself. He interprets the wand selection as a random process so he can determine the probabilities of different outcomes.
The wood types available are holly, elm, maple, and wenge. The core materials on offer are phoenix feather, unicorn hair, dragon scale, raven feather, and thestral tail.
Let A be the event that Harry is chosen by a wand made of holly and B be the event that he is chosen by a wand with a dragon scale core.
Answer: The probability of being chosen by a wand made of holly or a wand made of dragon scale core is 0.4 or 40%
Step-by-step explanation: What we have are probabilities of two events. The first is the probability that Harry Potter is chosen by a wand made of Holly which is P(A). The other event is the probability that Harry is chosen by a wand with a dragon scale which is P(B).
In other to calculate P(A), there is a total of four possibilities, (that is holly, elm, maple and wenge). Therefore, the probability is derived as;
P(A) = Number of required outcomes/Number of all possible outcomes
P(A) = 1/4 or (0.25)
To calculate P(B), there is a total of five possibilities (that is phoenix feather, unicorn hair, dragon scale, raven feather and thestral tail). Therefore the probability is derived as;
P(B) = Number of required outcomes/Number of all possible outcomes
P(B) = 1/5 or (0.20)
However, the question requires the probability of P(A or B).
First we derive the probability of being chosen by a wand made of holly AND one made of a dragon scale core. In other words we shall calculate the probability of P(A and B) which is derived as;
P(A and B) = P(A) x P(B)
P(A and ) = 1/4 x 1/5
P(A and B) = 1/20 (0.05)
The probability of P(A or B) can now be calculated as follows;
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = (0.25 +0.20) - 0.05
P(A or B) = 0.45 - 0.05
P(A or B) = 0.40
Therefore the probability that Harry Potter is chosen by a wand made of Holly or a wand with Dragon scale core is 0.4 or 40%
Answer: P( A or B) = 2/5
Step-by-step explanation:
25 points no I need help with math
Answer:
1. 23.55 in
2. 102.36 mm
Step-by-step explanation:
First, the circumference of a circle is written as: [tex]C=\pi d=2\pi r[/tex], where either equivalence works and d = diameter and r = radius.
1. We know that d = 7.5, so we just plug this into the equation:
[tex]C=\pi *7.5=3.14*7.5=23.55[/tex]
Thus, the circumference is 23.55 inches.
2. We know here that r = 16.3, so we can plug this into the other equivalence:
[tex]C=2*\pi *16.3=2*3.14*16.3=102.364[/tex] ≈ [tex]102.36[/tex]
Thus, the circumference is 102.36 millimeters.
Hope this helps!
Answer:
1. 23.55 inches
2. 102.36 millimeters
Step-by-step explanation:
1. Circumference = pi × d
3.14 × 7.5
= 23.55 in
2. Circumference = 2pi × r
2 × 3.15 × 16.3 = 102.364 mm