Question

What is the volume of the rectangular pyramid shown?

Height is 3.6mm
Length is 2.4mm
Width is 6.3mm

Answer 1

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

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

1. **Calculate the Base Area**:
The base area of a rectangular pyramid is the area of the rectangle at the base. The area of a rectangle is given by:

\[
\text{Base Area} = \text{Length} \times \text{Width}
\]

Substituting the given values:

\[
\text{Base Area} = 2.4 \, \text{mm} \times 6.3 \, \text{mm} = 15.12 \, \text{mm}^2
\]

2. **Calculate the Volume**:
Now, plug the base area and the height into the volume formula:

\[
\text{Volume} = \frac{1}{3} \times 15.12 \, \text{mm}^2 \times 3.6 \, \text{mm}
\]

\[
\text{Volume} = \frac{1}{3} \times 54.432 \, \text{mm}^3 = 18.144 \, \text{mm}^3
\]

Thus, the volume of the rectangular pyramid is approximately

\[
\boxed{18.144 \, \text{mm}^3}
\]