Question

I'm studying for my geometry exam and I'm having trouble finding the volume of a right rectangular pyramid. The pyramid has a height of 15 units and a base with length and width of 10 units and 12 units, respectively. Can you find the solution to this problem?

Answer 1

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

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

1. **Calculate the base area** of the rectangular base. The base area \( A \) can be found using the formula for the area of a rectangle:

\[
A = \text{length} \times \text{width}
\]

In this case, the length is 10 units, and the width is 12 units.

\[
A = 10 \times 12 = 120 \text{ square units}
\]

2. **Plug the base area and height into the volume formula**. The height of the pyramid is given as 15 units.

\[
\text{Volume} = \frac{1}{3} \times 120 \times 15
\]

3. **Calculate the volume**:

\[
\text{Volume} = \frac{1}{3} \times 120 \times 15 = \frac{1}{3} \times 1800 = 600 \text{ cubic units}
\]

So, the volume of the right rectangular pyramid is \( \boxed{600} \) cubic units.