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

98,400 cm3
98,400 cm cubed

10,933.33 cm3
10,933.33 cm cubed

32.67 cm3
32.67 cm cubed

32,800 cm3
32,800 cm cubed

Answer 1

To find the volume of a rectangular pyramid, you can use the formula:

\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

In this case, the base area can be found by multiplying the length and width:

\[
\text{Base Area} = \text{Length} \times \text{Width} = 32 \, \text{cm} \times 25 \, \text{cm} = 800 \, \text{cm}^2
\]

Now, use the height (altitude) of the pyramid, which is given as 41 cm:

\[
\text{Volume} = \frac{1}{3} \times 800 \, \text{cm}^2 \times 41 \, \text{cm}
\]

Calculating it step-by-step:

\[
\text{Volume} = \frac{1}{3} \times 800 \times 41
\]
\[
= \frac{1}{3} \times 32,800
\]
\[
= 10,933.33 \, \text{cm}^3
\]

Thus, the correct response is:

**10,933.33 cm³**.