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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### Problem Statement
**Question:**
What is the volume of a hemisphere with a radius of 44.9 m, rounded to the nearest tenth of a cubic meter?
---
To find the volume of a hemisphere, one can use the volume formula of a sphere \( V = \frac{4}{3} \pi r^3 \) and then take half of that volume since a hemisphere is half of a sphere. The formula for the volume of a hemisphere is:
\[ V = \frac{2}{3} \pi r^3 \]
Given:
- The radius \( r = 44.9 \) meters.
Substitute \( r \) into the formula:
\[ V = \frac{2}{3} \pi (44.9)^3 \]
Carrying out the calculations:
1. Calculate \( (44.9)^3 \).
2. Multiply the result by \( \pi \) (approximated as 3.1416 for the calculations).
3. Multiply by \( \frac{2}{3} \).
Finally, round the result to the nearest tenth.
(Note: Detailed calculations should typically involve the actual multiplication steps and rounding procedures, providing a better insight into using and approximating intermediate mathematical results to get accurate final outputs for educational purposes.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71ad11dc-25a4-4aef-afaf-b0879e57e72d%2F60a19223-9e4f-4fe4-ae4c-5e582662e3cb%2Ft6q9o7kg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:---
### Problem Statement
**Question:**
What is the volume of a hemisphere with a radius of 44.9 m, rounded to the nearest tenth of a cubic meter?
---
To find the volume of a hemisphere, one can use the volume formula of a sphere \( V = \frac{4}{3} \pi r^3 \) and then take half of that volume since a hemisphere is half of a sphere. The formula for the volume of a hemisphere is:
\[ V = \frac{2}{3} \pi r^3 \]
Given:
- The radius \( r = 44.9 \) meters.
Substitute \( r \) into the formula:
\[ V = \frac{2}{3} \pi (44.9)^3 \]
Carrying out the calculations:
1. Calculate \( (44.9)^3 \).
2. Multiply the result by \( \pi \) (approximated as 3.1416 for the calculations).
3. Multiply by \( \frac{2}{3} \).
Finally, round the result to the nearest tenth.
(Note: Detailed calculations should typically involve the actual multiplication steps and rounding procedures, providing a better insight into using and approximating intermediate mathematical results to get accurate final outputs for educational purposes.)
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