Roofing The roof of a building is in the shape of a pyramid having a square base 84 ft on each side. If the slant height of the roof is 60 ft, what would be the cost of the roofing material needed, at $0.95 per sq ft?
Roofing The roof of a building is in the shape of a pyramid having a square base 84 ft on each side. If the slant height of the roof is 60 ft, what would be the cost of the roofing material needed, at $0.95 per sq ft?
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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Question
![### Roofing Problem
The roof of a building is in the shape of a pyramid with a square base that measures 84 feet on each side. If the slant height of the roof is 60 feet, what would be the cost of the roofing material needed, if the material costs $0.95 per square foot?
#### Step-by-Step Solution:
1. **Calculate the Area of One Triangular Side:**
Each triangular side of the pyramid will have a base of 84 feet and a height (the slant height) of 60 feet.
The area \( A \) of one triangular side can be calculated using:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
\[
A = \frac{1}{2} \times 84 \, \text{ft} \times 60 \, \text{ft} = 2520 \, \text{sq ft}
\]
2. **Calculate the Total Surface Area of the Roof:**
Since it is a pyramid with a square base, there are four triangular sides.
\[
\text{Total Surface Area} = 4 \times 2520 \, \text{sq ft} = 10080 \, \text{sq ft}
\]
3. **Calculate the Cost of the Roofing Material:**
The cost per square foot is $0.95.
\[
\text{Total Cost} = 10080 \, \text{sq ft} \times 0.95 \, \frac{\text{\$}}{\text{sq ft}} = \$9576
\]
Therefore, the cost of the roofing material needed is \$9576.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae5712de-4746-4ba5-a688-ed474b665cfb%2F10bfeda6-bb5d-4568-93e5-3e7a87a01d03%2Fvqu2809.jpeg&w=3840&q=75)
Transcribed Image Text:### Roofing Problem
The roof of a building is in the shape of a pyramid with a square base that measures 84 feet on each side. If the slant height of the roof is 60 feet, what would be the cost of the roofing material needed, if the material costs $0.95 per square foot?
#### Step-by-Step Solution:
1. **Calculate the Area of One Triangular Side:**
Each triangular side of the pyramid will have a base of 84 feet and a height (the slant height) of 60 feet.
The area \( A \) of one triangular side can be calculated using:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
\[
A = \frac{1}{2} \times 84 \, \text{ft} \times 60 \, \text{ft} = 2520 \, \text{sq ft}
\]
2. **Calculate the Total Surface Area of the Roof:**
Since it is a pyramid with a square base, there are four triangular sides.
\[
\text{Total Surface Area} = 4 \times 2520 \, \text{sq ft} = 10080 \, \text{sq ft}
\]
3. **Calculate the Cost of the Roofing Material:**
The cost per square foot is $0.95.
\[
\text{Total Cost} = 10080 \, \text{sq ft} \times 0.95 \, \frac{\text{\$}}{\text{sq ft}} = \$9576
\]
Therefore, the cost of the roofing material needed is \$9576.
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