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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![**Question**
What is the volume of a hemisphere with a radius of 4.3 cm, rounded to the nearest tenth of a cubic centimeter?
**Solution**
To find the volume of a hemisphere, you can start with the formula for the volume of a sphere and then divide by two because a hemisphere is half of a sphere.
The formula for the volume of a sphere is:
\[ V = \frac{4}{3} \pi r^3 \]
For a hemisphere:
\[ V_{hemisphere} = \frac{1}{2} \left( \frac{4}{3} \pi r^3 \right) \]
Given the radius \( r = 4.3 \) cm, we can substitute this value into the formula:
\[ V_{hemisphere} = \frac{1}{2} \left( \frac{4}{3} \pi (4.3)^3 \right) \]
First, calculate \( (4.3)^3 \):
\[ 4.3^3 \approx 79.507 \]
Next, multiply by \(\pi \):
\[ \pi \times 79.507 \approx 249.831 \]
Then, continue with the formula:
\[ V_{hemisphere} = \frac{1}{2} \left( \frac{4}{3} \times 249.831 \right) \]
\[ = \frac{1}{2} \left( \frac{4 \times 249.831}{3} \right) \]
\[ = \frac{1}{2} \left( 333.108 \right) \]
\[ = 166.554 \]
Rounded to the nearest tenth, the volume of the hemisphere is approximately:
\[ 166.6 \; \text{cubic centimeters} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71ad11dc-25a4-4aef-afaf-b0879e57e72d%2F845bc66a-b86f-4ed5-8a65-7321fa933801%2Fu39kkzj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question**
What is the volume of a hemisphere with a radius of 4.3 cm, rounded to the nearest tenth of a cubic centimeter?
**Solution**
To find the volume of a hemisphere, you can start with the formula for the volume of a sphere and then divide by two because a hemisphere is half of a sphere.
The formula for the volume of a sphere is:
\[ V = \frac{4}{3} \pi r^3 \]
For a hemisphere:
\[ V_{hemisphere} = \frac{1}{2} \left( \frac{4}{3} \pi r^3 \right) \]
Given the radius \( r = 4.3 \) cm, we can substitute this value into the formula:
\[ V_{hemisphere} = \frac{1}{2} \left( \frac{4}{3} \pi (4.3)^3 \right) \]
First, calculate \( (4.3)^3 \):
\[ 4.3^3 \approx 79.507 \]
Next, multiply by \(\pi \):
\[ \pi \times 79.507 \approx 249.831 \]
Then, continue with the formula:
\[ V_{hemisphere} = \frac{1}{2} \left( \frac{4}{3} \times 249.831 \right) \]
\[ = \frac{1}{2} \left( \frac{4 \times 249.831}{3} \right) \]
\[ = \frac{1}{2} \left( 333.108 \right) \]
\[ = 166.554 \]
Rounded to the nearest tenth, the volume of the hemisphere is approximately:
\[ 166.6 \; \text{cubic centimeters} \]
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