Question
Volume of Pyramids Practice
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Question
Cecilia built a model pyramid out of foam. Her model is 20 inches high, with a rectangular base that is 8 inches long and 12 inches wide. What is the volume of her model in cubic inches?(1 point)
in3
Remaining Attempts : 3
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Answers
GPT-4o mini
To find the volume of a pyramid, you can use the formula:
\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Given that Cecilia's pyramid has a rectangular base, we can calculate the base area by multiplying the length and width of the base:
\[
\text{Base Area} = \text{Length} \times \text{Width} = 8 \, \text{inches} \times 12 \, \text{inches} = 96 \, \text{square inches}
\]
Next, we can plug the base area and height into the volume formula. The height of the pyramid is given as 20 inches:
\[
\text{Volume} = \frac{1}{3} \times 96 \, \text{in}^2 \times 20 \, \text{in}
\]
Now, let's do the calculation:
\[
\text{Volume} = \frac{1}{3} \times 96 \times 20 = \frac{1920}{3} = 640 \, \text{cubic inches}
\]
So, the volume of Cecilia's model pyramid is
\[
640 \, \text{in}^3
\]
\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Given that Cecilia's pyramid has a rectangular base, we can calculate the base area by multiplying the length and width of the base:
\[
\text{Base Area} = \text{Length} \times \text{Width} = 8 \, \text{inches} \times 12 \, \text{inches} = 96 \, \text{square inches}
\]
Next, we can plug the base area and height into the volume formula. The height of the pyramid is given as 20 inches:
\[
\text{Volume} = \frac{1}{3} \times 96 \, \text{in}^2 \times 20 \, \text{in}
\]
Now, let's do the calculation:
\[
\text{Volume} = \frac{1}{3} \times 96 \times 20 = \frac{1920}{3} = 640 \, \text{cubic inches}
\]
So, the volume of Cecilia's model pyramid is
\[
640 \, \text{in}^3
\]