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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![**Find the Volume of the Pyramid**
In the diagram, we have a pyramid with a rectangular base. The base measures 18 feet by 13 feet, and the height of the pyramid, which is the perpendicular distance from the base to the apex (top point), is 15 feet.
To find the volume of a pyramid, we use the formula:
\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
1. **Calculate the base area:**
\[ \text{Base Area} = \text{Length} \times \text{Width}\]
\[ \text{Base Area} = 18 \, \text{ft} \times 13 \, \text{ft} = 234 \, \text{ft}^2 \]
2. **Calculate the volume:**
\[ \text{Volume} = \frac{1}{3} \times 234 \, \text{ft}^2 \times 15 \, \text{ft} \]
\[ \text{Volume} = \frac{1}{3} \times 3510 \, \text{ft}^3 \]
\[ \text{Volume} = 1170 \, \text{ft}^3 \]
Therefore, the volume of the pyramid is \( 1170 \, \text{ft}^3 \).
The diagram shows the pyramid from an angle that visualizes its three dimensions. The dotted lines represent the hidden edges and the right angle marks indicate the positions of the height which intersects the base at a right angle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8cc5b47-1a8c-416c-961a-08ac39ec1d30%2Fcdfedcc7-b3d1-492c-bf16-caf72aa72524%2F0ib59fm.jpeg&w=3840&q=75)
Transcribed Image Text:**Find the Volume of the Pyramid**
In the diagram, we have a pyramid with a rectangular base. The base measures 18 feet by 13 feet, and the height of the pyramid, which is the perpendicular distance from the base to the apex (top point), is 15 feet.
To find the volume of a pyramid, we use the formula:
\[ \text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]
1. **Calculate the base area:**
\[ \text{Base Area} = \text{Length} \times \text{Width}\]
\[ \text{Base Area} = 18 \, \text{ft} \times 13 \, \text{ft} = 234 \, \text{ft}^2 \]
2. **Calculate the volume:**
\[ \text{Volume} = \frac{1}{3} \times 234 \, \text{ft}^2 \times 15 \, \text{ft} \]
\[ \text{Volume} = \frac{1}{3} \times 3510 \, \text{ft}^3 \]
\[ \text{Volume} = 1170 \, \text{ft}^3 \]
Therefore, the volume of the pyramid is \( 1170 \, \text{ft}^3 \).
The diagram shows the pyramid from an angle that visualizes its three dimensions. The dotted lines represent the hidden edges and the right angle marks indicate the positions of the height which intersects the base at a right angle.
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