Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter22: Introduction To Percents
Section: Chapter Questions
Problem 1A
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Question
![**Question:**
What is the volume of a hemisphere with a radius of 6.1 ft, rounded to the nearest tenth of a cubic foot?
**Explanation:**
To find the volume of a hemisphere, you can use the formula for the volume of a sphere and then divide by 2.
The formula for the volume of a sphere is:
\[ V = \frac{4}{3} \pi r^3 \]
For a hemisphere:
\[ V_{\text{hemisphere}} = \frac{1}{2} \left( \frac{4}{3} \pi r^3 \right) \]
Given:
\[ r = 6.1 \text{ ft} \]
First, calculate the volume of the sphere:
\[ V = \frac{4}{3} \pi (6.1)^3 \]
Then, divide by 2 to get the volume of the hemisphere:
\[ V_{\text{hemisphere}} = \frac{1}{2} \left( \frac{4}{3} \pi (6.1)^3 \right) \]
After performing these calculations, round the result to the nearest tenth.
**Calculation Steps:**
1. Cube the radius:
\[ (6.1)^3 = 226.981 \]
2. Multiply by \(\pi\) and \(\frac{4}{3}\):
\[ \frac{4}{3} \pi \times 226.981 \approx 951.73 \]
3. Divide by 2 to get the hemisphere volume:
\[ V_{\text{hemisphere}} \approx \frac{951.73}{2} \approx 475.9 \text{ cubic feet} \]
Thus, the volume of the hemisphere is approximately **475.9 cubic feet**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F71ad11dc-25a4-4aef-afaf-b0879e57e72d%2F97fd264a-22f8-43ab-a8bf-5a6129d75a72%2Fvj45i0e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
What is the volume of a hemisphere with a radius of 6.1 ft, rounded to the nearest tenth of a cubic foot?
**Explanation:**
To find the volume of a hemisphere, you can use the formula for the volume of a sphere and then divide by 2.
The formula for the volume of a sphere is:
\[ V = \frac{4}{3} \pi r^3 \]
For a hemisphere:
\[ V_{\text{hemisphere}} = \frac{1}{2} \left( \frac{4}{3} \pi r^3 \right) \]
Given:
\[ r = 6.1 \text{ ft} \]
First, calculate the volume of the sphere:
\[ V = \frac{4}{3} \pi (6.1)^3 \]
Then, divide by 2 to get the volume of the hemisphere:
\[ V_{\text{hemisphere}} = \frac{1}{2} \left( \frac{4}{3} \pi (6.1)^3 \right) \]
After performing these calculations, round the result to the nearest tenth.
**Calculation Steps:**
1. Cube the radius:
\[ (6.1)^3 = 226.981 \]
2. Multiply by \(\pi\) and \(\frac{4}{3}\):
\[ \frac{4}{3} \pi \times 226.981 \approx 951.73 \]
3. Divide by 2 to get the hemisphere volume:
\[ V_{\text{hemisphere}} \approx \frac{951.73}{2} \approx 475.9 \text{ cubic feet} \]
Thus, the volume of the hemisphere is approximately **475.9 cubic feet**.
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