Question
Right Rectangular Prisms & Pyramids Unit Test
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Question
What is the volume of a rectangular pyramid with a length of 32 cm, a width of 25 cm, and an altitude of 41 cm?(1 point)
Responses
10,933.33 cm3
10,933.33 cm cubed
32.67 cm3
32.67 cm cubed
32,800 cm3
32,800 cm cubed
98,400 cm3
98,400 cm cubed
Answers
GPT-4o mini
To calculate the volume of a rectangular pyramid, you can use the formula:
\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Where the base area (for a rectangular base) is calculated as:
\[
\text{Base Area} = \text{Length} \times \text{Width}
\]
Plugging in the dimensions:
- Length = 32 cm
- Width = 25 cm
- Height = 41 cm
First, calculate the base area:
\[
\text{Base Area} = 32 \, \text{cm} \times 25 \, \text{cm} = 800 \, \text{cm}^2
\]
Next, calculate the volume:
\[
\text{Volume} = \frac{1}{3} \times 800 \, \text{cm}^2 \times 41 \, \text{cm}
\]
\[
\text{Volume} = \frac{1}{3} \times 32,800 \, \text{cm}^3
\]
\[
\text{Volume} = 10,933.33 \, \text{cm}^3
\]
Therefore, the correct answer is:
**10,933.33 cm³** (or **10,933.33 cm cubed**)
\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Where the base area (for a rectangular base) is calculated as:
\[
\text{Base Area} = \text{Length} \times \text{Width}
\]
Plugging in the dimensions:
- Length = 32 cm
- Width = 25 cm
- Height = 41 cm
First, calculate the base area:
\[
\text{Base Area} = 32 \, \text{cm} \times 25 \, \text{cm} = 800 \, \text{cm}^2
\]
Next, calculate the volume:
\[
\text{Volume} = \frac{1}{3} \times 800 \, \text{cm}^2 \times 41 \, \text{cm}
\]
\[
\text{Volume} = \frac{1}{3} \times 32,800 \, \text{cm}^3
\]
\[
\text{Volume} = 10,933.33 \, \text{cm}^3
\]
Therefore, the correct answer is:
**10,933.33 cm³** (or **10,933.33 cm cubed**)