Question

The area of the base of a triangular pyramid is 75 square inches. The height of the pyramid is 14 inches.


What is the volume of the triangular pyramid in cubic inches?

(1 point)
Responses

525 inches
525 inches

1,050 inches
1,050 inches

350 inches
350 inches

375 inches

Answer 1

The formula for the volume \( V \) of a pyramid is given by:

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

In this case, the base area is 75 square inches and the height is 14 inches. Plugging in these values we get:

\[
V = \frac{1}{3} \times 75 \times 14
\]

Calculating this step by step:

1. First, calculate \( 75 \times 14 \):

\[
75 \times 14 = 1050
\]

2. Then, calculate \( \frac{1}{3} \times 1050 \):

\[
\frac{1}{3} \times 1050 = 350
\]

Therefore, the volume of the triangular pyramid is:

\[
\boxed{350} \text{ cubic inches}
\]