Question

What is the volume of the rectangular pyramid?

Width: 4 cm

Length: 3 cm

Height: 12 cm

Answer 1

The volume \( V \) of a rectangular pyramid can be calculated using the formula:

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

For a rectangular pyramid, the base area is given by the width \( w \) and length \( l \):

\[
\text{Base Area} = w \times l
\]

In this case, the width is 4 cm, the length is 3 cm, and the height is 12 cm.

First, calculate the base area:

\[
\text{Base Area} = 4 \, \text{cm} \times 3 \, \text{cm} = 12 \, \text{cm}^2
\]

Now, use the volume formula:

\[
V = \frac{1}{3} \times 12 \, \text{cm}^2 \times 12 \, \text{cm}
\]

Calculating the volume:

\[
V = \frac{1}{3} \times 144 \, \text{cm}^3 = 48 \, \text{cm}^3
\]

Thus, the volume of the rectangular pyramid is

\[
\boxed{48 \, \text{cm}^3}
\]