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

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