Question

A stereo system in the shape of a triangular pyramid has a height of 7.5 inches. The area of the base of the speaker is 12 square inches. What is the volume of the speaker in cubic inches?

Answer 1

To find the volume of a triangular pyramid (also known as a tetrahedron), we can use the following formula:

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

Given:
- Height \( h = 7.5 \) inches
- Base Area \( A = 12 \) square inches

Now, substitute the values into the volume formula:

\[
V = \frac{1}{3} \times 12 \times 7.5
\]

Now calculate the multiplication:

\[
12 \times 7.5 = 90
\]

Now substitute back into the volume formula:

\[
V = \frac{1}{3} \times 90
\]

Calculate the final volume:

\[
V = 30
\]

Thus, the volume of the stereo system is

\[
\boxed{30} \text{ cubic inches}.
\]