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), you can use the formula:

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

In this case, the area of the base is given as 12 square inches and the height is 7.5 inches. Plugging in the values:

\[
V = \frac{1}{3} \times 12 \, \text{sq in} \times 7.5 \, \text{in}
\]

Calculating this step by step:

1. Multiply the base area by the height:
\[
12 \times 7.5 = 90
\]

2. Now, multiply by \(\frac{1}{3}\):
\[
V = \frac{1}{3} \times 90 = 30
\]

Therefore, the volume of the speaker is:

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