15. In the diagram below, a right circular cone has a diameter of 8 inches and a height of 12 inches. What is the volume of the cone to the nearest cubicinch? 8 Inches 12 Inches A. 603 B. 481 C. 201 D. 804
15. In the diagram below, a right circular cone has a diameter of 8 inches and a height of 12 inches. What is the volume of the cone to the nearest cubicinch? 8 Inches 12 Inches A. 603 B. 481 C. 201 D. 804
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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What is the volume
![### Cone Volume Problem
#### Question:
15. In the diagram below, a right circular cone has a diameter of 8 inches and a height of 12 inches. What is the volume of the cone to the nearest cubic inch?
#### Diagram Description:
- The diagram is a right circular cone.
- The cone has a diameter of 8 inches.
- The height of the cone is 12 inches.
#### Diagram:
- A right circular cone is shown with a base diameter of 8 inches.
- A perpendicular height from the base to the apex is 12 inches.
#### Question Options:
- A. 603
- B. 481
- C. 201
- D. 804
To solve the problem, use the formula for the volume of a cone:
\[ \text{Volume} = \frac{1}{3} \pi r^2 h \]
Where:
- \( \pi \) (pi) is approximately 3.14159.
- \( r \) is the radius of the base.
- \( h \) is the height of the cone.
Given data:
- Diameter = 8 inches, so Radius \( r = \frac{8}{2} = 4 \) inches.
- Height \( h = 12 \) inches.
Now, substitute the values into the volume formula:
\[ \text{Volume} = \frac{1}{3} \pi (4)^2 (12) \]
\[ \text{Volume} = \frac{1}{3} \pi (16) (12) \]
\[ \text{Volume} = \frac{1}{3} \pi (192) \]
\[ \text{Volume} \approx \frac{1}{3} (3.14159) (192) \]
\[ \text{Volume} \approx 201.062 \]
Hence, the volume of the cone is approximately 201 cubic inches.
### Correct Option:
- C. 201](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6756c5c2-608f-4015-b13f-deb910f8c3e1%2Fe54325e7-6e69-4d30-a250-4b093153bb00%2Fkciv4c_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Cone Volume Problem
#### Question:
15. In the diagram below, a right circular cone has a diameter of 8 inches and a height of 12 inches. What is the volume of the cone to the nearest cubic inch?
#### Diagram Description:
- The diagram is a right circular cone.
- The cone has a diameter of 8 inches.
- The height of the cone is 12 inches.
#### Diagram:
- A right circular cone is shown with a base diameter of 8 inches.
- A perpendicular height from the base to the apex is 12 inches.
#### Question Options:
- A. 603
- B. 481
- C. 201
- D. 804
To solve the problem, use the formula for the volume of a cone:
\[ \text{Volume} = \frac{1}{3} \pi r^2 h \]
Where:
- \( \pi \) (pi) is approximately 3.14159.
- \( r \) is the radius of the base.
- \( h \) is the height of the cone.
Given data:
- Diameter = 8 inches, so Radius \( r = \frac{8}{2} = 4 \) inches.
- Height \( h = 12 \) inches.
Now, substitute the values into the volume formula:
\[ \text{Volume} = \frac{1}{3} \pi (4)^2 (12) \]
\[ \text{Volume} = \frac{1}{3} \pi (16) (12) \]
\[ \text{Volume} = \frac{1}{3} \pi (192) \]
\[ \text{Volume} \approx \frac{1}{3} (3.14159) (192) \]
\[ \text{Volume} \approx 201.062 \]
Hence, the volume of the cone is approximately 201 cubic inches.
### Correct Option:
- C. 201
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