Question
Volume of Pyramids Quick Check
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Question
A construction company is digging a drainage trench. It makes the shape of an upside-down rectangular pyramid. The top opening will be 30 ft. wide by 250 ft. long, and the deepest part in the middle will be 15 ft. What is the capacity for this trench?(1 point)
Responses
98.33 ft.3
98.33 feet cubed
337,500 ft.3
337,500 feet cubed
112,500 ft.3
112,500 feet cubed
37,500 ft.3
37,500 feet cubed
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5 of 55 of 5 Items
Question
A construction company is digging a drainage trench. It makes the shape of an upside-down rectangular pyramid. The top opening will be 30 ft. wide by 250 ft. long, and the deepest part in the middle will be 15 ft. What is the capacity for this trench?(1 point)
Responses
98.33 ft.3
98.33 feet cubed
337,500 ft.3
337,500 feet cubed
112,500 ft.3
112,500 feet cubed
37,500 ft.3
37,500 feet cubed
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Answers
GPT-4o mini
To find the volume of an upside-down rectangular pyramid (a frustum of a pyramid), you can use the formula for the volume of a rectangular pyramid:
\[
V = \frac{1}{3} \times \text{base area} \times \text{height}
\]
In this case, the base area is the area of the rectangle at the top opening of the trench. The dimensions are:
- Width = 30 ft
- Length = 250 ft
- Height = 15 ft
First, we calculate the base area:
\[
\text{Base Area} = \text{Width} \times \text{Length} = 30 \, \text{ft} \times 250 \, \text{ft} = 7500 \, \text{ft}^2
\]
Next, we apply the height:
\[
\text{Height} = 15 \, \text{ft}
\]
Now we can calculate the volume:
\[
V = \frac{1}{3} \times 7500 \, \text{ft}^2 \times 15 \, \text{ft}
\]
Calculating that gives:
\[
V = \frac{1}{3} \times 7500 \times 15 = \frac{112500}{3} = 37500 \, \text{ft}^3
\]
Therefore, the capacity of the trench is:
**37,500 ft³**
So the correct response is:
**37,500 ft³**.
\[
V = \frac{1}{3} \times \text{base area} \times \text{height}
\]
In this case, the base area is the area of the rectangle at the top opening of the trench. The dimensions are:
- Width = 30 ft
- Length = 250 ft
- Height = 15 ft
First, we calculate the base area:
\[
\text{Base Area} = \text{Width} \times \text{Length} = 30 \, \text{ft} \times 250 \, \text{ft} = 7500 \, \text{ft}^2
\]
Next, we apply the height:
\[
\text{Height} = 15 \, \text{ft}
\]
Now we can calculate the volume:
\[
V = \frac{1}{3} \times 7500 \, \text{ft}^2 \times 15 \, \text{ft}
\]
Calculating that gives:
\[
V = \frac{1}{3} \times 7500 \times 15 = \frac{112500}{3} = 37500 \, \text{ft}^3
\]
Therefore, the capacity of the trench is:
**37,500 ft³**
So the correct response is:
**37,500 ft³**.