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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![### Finding the Height of a Pyramid
**Problem Statement:**
Find the height of the given figure when the volume is 15 cubic yards (15 yd³).
**Figure Explanation:**
The figure shown is a pyramid with a square base. Each side of the base measures 3 yards (3 yd).
**Volume Formula:**
To find the height of a pyramid, we use the formula for the volume of a pyramid, which is given by:
\[ V = \frac{1}{3} B h \]
Where:
- \( V \) is the volume of the pyramid.
- \( B \) is the area of the base.
- \( h \) is the height of the pyramid.
**Given:**
- Volume (V) = 15 yd³
- Length of base side = 3 yd
**Steps to Find the Height:**
1. Calculate the area of the base (B):
\[
B = \text{side} \times \text{side} = 3 \, \text{yd} \times 3 \, \text{yd} = 9 \, \text{yd}^2
\]
2. Plug the known values into the volume formula and solve for the height (h):
\[
15 \, \text{yd}^3 = \frac{1}{3} (9 \, \text{yd}^2) \times h
\]
3. Simplify the equation:
\[
15 = 3h
\]
4. Solve for \( h \):
\[
h = \frac{15}{3} = 5 \, \text{yd}
\]
**Answer:**
\[
\text{height} = 5 \, \text{yd}
\]
### Diagram Explanation:
The diagram shown is a 3D representation of a pyramid with a square base. The base of the pyramid is indicated as being 3 yards on each side. An inner red line denotes the height of the pyramid, which is perpendicular from the base to the apex.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e046ea4-05f5-4640-8a37-b1c9a5ef5104%2Fd772e89d-8947-44d5-8587-acc679f35d05%2Fpjke92_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Finding the Height of a Pyramid
**Problem Statement:**
Find the height of the given figure when the volume is 15 cubic yards (15 yd³).
**Figure Explanation:**
The figure shown is a pyramid with a square base. Each side of the base measures 3 yards (3 yd).
**Volume Formula:**
To find the height of a pyramid, we use the formula for the volume of a pyramid, which is given by:
\[ V = \frac{1}{3} B h \]
Where:
- \( V \) is the volume of the pyramid.
- \( B \) is the area of the base.
- \( h \) is the height of the pyramid.
**Given:**
- Volume (V) = 15 yd³
- Length of base side = 3 yd
**Steps to Find the Height:**
1. Calculate the area of the base (B):
\[
B = \text{side} \times \text{side} = 3 \, \text{yd} \times 3 \, \text{yd} = 9 \, \text{yd}^2
\]
2. Plug the known values into the volume formula and solve for the height (h):
\[
15 \, \text{yd}^3 = \frac{1}{3} (9 \, \text{yd}^2) \times h
\]
3. Simplify the equation:
\[
15 = 3h
\]
4. Solve for \( h \):
\[
h = \frac{15}{3} = 5 \, \text{yd}
\]
**Answer:**
\[
\text{height} = 5 \, \text{yd}
\]
### Diagram Explanation:
The diagram shown is a 3D representation of a pyramid with a square base. The base of the pyramid is indicated as being 3 yards on each side. An inner red line denotes the height of the pyramid, which is perpendicular from the base to the apex.
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