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What is the volume of a sphere whose radius is 14.86? Use л = 3.14 as needed. Round to two decimal places as needed.

What is the volume of a sphere whose radius is 14.86? Use л = 3.14 as needed. Round to two decimal places as needed.

Elementary Geometry For College Students, 7e
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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### Calculating the Volume of a Sphere with Given Radius #### Problem Statement: What is the volume of a sphere whose radius is 14.86? #### Given: - Radius (\(r\)): 14.86 - Use \(\pi = 3.14\) as needed. - Round to two decimal places as needed. #### Solution: To find the volume of a sphere, we use the formula: \[ V = \frac{4}{3} \pi r^3 \] 1. Substitute the given radius and value of \(\pi\) into the formula: \[ V = \frac{4}{3} \times 3.14 \times (14.86)^3 \] 2. Calculate the cube of the radius: \[ (14.86)^3 \approx 3281.91 \] 3. Multiply by \(\pi\): \[ 3.14 \times 3281.91 \approx 10366.20 \] 4. Multiply by \(\frac{4}{3}\): \[ V = \frac{4}{3} \times 10366.20 \approx 13821.60 \] 5. Round the result to two decimal places: \[ V \approx 13821.60 \, \text{cubic units} \] Therefore, the volume of the sphere is approximately **13821.60 cubic units**.
Transcribed Image Text:### Calculating the Volume of a Sphere with Given Radius #### Problem Statement: What is the volume of a sphere whose radius is 14.86? #### Given: - Radius (\(r\)): 14.86 - Use \(\pi = 3.14\) as needed. - Round to two decimal places as needed. #### Solution: To find the volume of a sphere, we use the formula: \[ V = \frac{4}{3} \pi r^3 \] 1. Substitute the given radius and value of \(\pi\) into the formula: \[ V = \frac{4}{3} \times 3.14 \times (14.86)^3 \] 2. Calculate the cube of the radius: \[ (14.86)^3 \approx 3281.91 \] 3. Multiply by \(\pi\): \[ 3.14 \times 3281.91 \approx 10366.20 \] 4. Multiply by \(\frac{4}{3}\): \[ V = \frac{4}{3} \times 10366.20 \approx 13821.60 \] 5. Round the result to two decimal places: \[ V \approx 13821.60 \, \text{cubic units} \] Therefore, the volume of the sphere is approximately **13821.60 cubic units**.
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