A company makes cones out of solid foam. Each cone has a height of 15 inches, and its base has a diameter of 3 inches. How much foam is needed to make 160 cones? Use 3.14 for t, and do not round your answer.
A company makes cones out of solid foam. Each cone has a height of 15 inches, and its base has a diameter of 3 inches. How much foam is needed to make 160 cones? Use 3.14 for t, and do not round your answer.
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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![### Volume of Solid Foam Cones Calculation
**Question:**
A company makes cones out of solid foam. Each cone has a height of 15 inches, and its base has a diameter of 3 inches. How much foam is needed to make 160 cones?
Use 3.14 for \( \pi \), and do not round your answer.
**Solution:**
To find the volume of a single cone, we use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
1. Convert the diameter to the radius:
\[ \text{Radius} = \frac{3}{2} = 1.5 \text{ inches} \]
2. Substitute the radius (1.5 inches) and the height (15 inches) into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (1.5)^2 \times 15 \]
\[ V = \frac{1}{3} \times 3.14 \times 2.25 \times 15 \]
\[ V = \frac{1}{3} \times 3.14 \times 33.75 \]
\[ V = 35.325 \text{ cubic inches} \]
3. To find the total amount of foam needed for 160 cones:
\[ \text{Total Volume} = 35.325 \times 160 \]
\[ \text{Total Volume} = 5,652 \text{ cubic inches} \]
### Answer:
The amount of foam needed to make 160 cones is 5,652 cubic inches.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2f0cb9e0-878b-46ea-a9a5-5d8e401495e2%2Fd5e6782c-7499-4048-a89a-07c8603c8c11%2Fzlgcdo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Volume of Solid Foam Cones Calculation
**Question:**
A company makes cones out of solid foam. Each cone has a height of 15 inches, and its base has a diameter of 3 inches. How much foam is needed to make 160 cones?
Use 3.14 for \( \pi \), and do not round your answer.
**Solution:**
To find the volume of a single cone, we use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
1. Convert the diameter to the radius:
\[ \text{Radius} = \frac{3}{2} = 1.5 \text{ inches} \]
2. Substitute the radius (1.5 inches) and the height (15 inches) into the formula:
\[ V = \frac{1}{3} \times 3.14 \times (1.5)^2 \times 15 \]
\[ V = \frac{1}{3} \times 3.14 \times 2.25 \times 15 \]
\[ V = \frac{1}{3} \times 3.14 \times 33.75 \]
\[ V = 35.325 \text{ cubic inches} \]
3. To find the total amount of foam needed for 160 cones:
\[ \text{Total Volume} = 35.325 \times 160 \]
\[ \text{Total Volume} = 5,652 \text{ cubic inches} \]
### Answer:
The amount of foam needed to make 160 cones is 5,652 cubic inches.
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