In the chart below, the value of $ r $ (radius), $ V $ (volume), or $ S $ (surface area) is given for a particular sphere. Find the remaining two values. Leave $\pi$ in your answers.| $ r $ | $ V $ | $ S $ ||-----------|---------|---------|| 13 in. | | |The volume of a sphere with radius 13 is $\boxed{}$.(Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact answer, using $\pi$ as needed.)The surface area of a sphere with radius 13 is $\boxed{}$.(Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact answer, using $\pi$ as needed.)Enter your answer in each of the answer boxes.

Answered: the value of r (radius), V (volume), or…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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In the chart below, the value of $ r $ (radius), $ V $ (volume), or $ S $ (surface area) is given for a particular sphere. Find the remaining two values. Leave $\pi$ in your answers.

| $ r $ | $ V $ | $ S $ |
|-----------|---------|---------|
| 13 in. | | |

The volume of a sphere with radius 13 is $\boxed{}$.

(Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact answer, using $\pi$ as needed.)

The surface area of a sphere with radius 13 is $\boxed{}$.

(Simplify your answer. Use integers or fractions for any numbers in the expression. Type an exact answer, using $\pi$ as needed.)

Enter your answer in each of the answer boxes.

Expert Solution

Step 1

$R a d i u s o f t h e s p h e r e = r = 13 i n c h e s F o r m u l a f o r t h e v o l u m e o f t h e s p h e r e i s g i v e n b y - V o l u m e = V = \frac{4}{3} {πr}^{3} V = \frac{4}{3} \times π \times {(13)}^{3} V = \frac{8788}{3} π {cm}^{3} (in terms of π) V = \frac{8788}{3} \times \frac{22}{7} V = \frac{193336}{21} {cm}^{3} (Answer)$

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