ind the volume of a pyramid with a square base, where the side lengtl of the base is 10.6 in and the height of the pyramid is 12.3 in. Round rour answer to the nearest tenth of a cubic inch.
ind the volume of a pyramid with a square base, where the side lengtl of the base is 10.6 in and the height of the pyramid is 12.3 in. Round rour answer to the nearest tenth of a cubic inch.
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 a Pyramid Calculation**
**Problem Statement:**
Find the volume of a pyramid with a square base, where the side length of the base is 10.6 inches and the height of the pyramid is 12.3 inches. Round your answer to the nearest tenth of a cubic inch.
**Solution:**
To find the volume of a pyramid, we use the formula:
\[ V = \frac{1}{3} B h \]
where \(B\) is the area of the base and \(h\) is the height.
1. Calculate the area of the base (\(B\)):
\[ B = \text{side length}^2 \]
\[ B = 10.6 \, \text{in} \times 10.6 \, \text{in} \]
\[ B = 112.36 \, \text{in}^2 \]
2. Plug the area of the base and the height into the volume formula:
\[ V = \frac{1}{3} \times 112.36 \, \text{in}^2 \times 12.3 \, \text{in} \]
\[ V = \frac{1}{3} \times 1381.028 \, \text{in}^3 \]
\[ V = 460.3426 \, \text{in}^3 \]
3. Round the volume to the nearest tenth:
\[ V \approx 460.3 \, \text{in}^3 \]
Thus, the volume of the pyramid is approximately **460.3 cubic inches**.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8558c5d0-725b-4408-8602-a637263c1a48%2F22000158-ed62-4a43-b479-6b154eda602a%2Fltfuvuf_processed.png&w=3840&q=75)
Transcribed Image Text:**Volume of a Pyramid Calculation**
**Problem Statement:**
Find the volume of a pyramid with a square base, where the side length of the base is 10.6 inches and the height of the pyramid is 12.3 inches. Round your answer to the nearest tenth of a cubic inch.
**Solution:**
To find the volume of a pyramid, we use the formula:
\[ V = \frac{1}{3} B h \]
where \(B\) is the area of the base and \(h\) is the height.
1. Calculate the area of the base (\(B\)):
\[ B = \text{side length}^2 \]
\[ B = 10.6 \, \text{in} \times 10.6 \, \text{in} \]
\[ B = 112.36 \, \text{in}^2 \]
2. Plug the area of the base and the height into the volume formula:
\[ V = \frac{1}{3} \times 112.36 \, \text{in}^2 \times 12.3 \, \text{in} \]
\[ V = \frac{1}{3} \times 1381.028 \, \text{in}^3 \]
\[ V = 460.3426 \, \text{in}^3 \]
3. Round the volume to the nearest tenth:
\[ V \approx 460.3 \, \text{in}^3 \]
Thus, the volume of the pyramid is approximately **460.3 cubic inches**.
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