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 Calculation of a Cone-Shaped Grain Silo**
**Problem Statement:**
A grain silo is shaped like a cone, as shown in the diagram. If the height of the grain in the silo is 30 feet, what is the exact volume of grain in the silo? [6 points]
**Diagram Explanation:**
The diagram depicts a cone-shaped silo. The dimensions provided in the diagram are:
- Height of the entire silo: 60 feet
- Radius of the base of the silo: 20 feet
However, the grain fills only half of the silo's height, which is 30 feet.
To calculate the volume of the cone-shaped portion filled with grain, we will use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( V \) is the volume
- \( r \) is the radius of the base of the cone
- \( h \) is the height of the cone
Given that:
- Radius \( r \) = 20 feet
- Height \( h \) = 30 feet
The exact volume of the grain in the silo can thus be calculated by substituting these values into the formula.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5cefd63-ef89-4ce7-aa2e-589f028ea473%2Fdf503428-a820-42f5-9a19-fa47fab51b06%2Ff9kbz5.jpeg&w=3840&q=75)
Transcribed Image Text:**Volume Calculation of a Cone-Shaped Grain Silo**
**Problem Statement:**
A grain silo is shaped like a cone, as shown in the diagram. If the height of the grain in the silo is 30 feet, what is the exact volume of grain in the silo? [6 points]
**Diagram Explanation:**
The diagram depicts a cone-shaped silo. The dimensions provided in the diagram are:
- Height of the entire silo: 60 feet
- Radius of the base of the silo: 20 feet
However, the grain fills only half of the silo's height, which is 30 feet.
To calculate the volume of the cone-shaped portion filled with grain, we will use the formula for the volume of a cone:
\[ V = \frac{1}{3} \pi r^2 h \]
where:
- \( V \) is the volume
- \( r \) is the radius of the base of the cone
- \( h \) is the height of the cone
Given that:
- Radius \( r \) = 20 feet
- Height \( h \) = 30 feet
The exact volume of the grain in the silo can thus be calculated by substituting these values into the formula.
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