Question

The area of the base of a triangular pyramid is 60 square inches. The height of the pyramid is 13 inches. What is the volume of the triangular pyramid in cubic inches? A 390 in.3 260 in.3 780 in.3 130 in. step by step on how you got the answer

Answer 1

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

\[
V = \frac{1}{3} \times B \times h
\]

where:
- \( V \) is the volume,
- \( B \) is the area of the base, and
- \( h \) is the height of the pyramid.

Given:
- The area of the base \( B = 60 \) square inches
- The height \( h = 13 \) inches

We can now substitute these values into the volume formula:

\[
V = \frac{1}{3} \times 60 \times 13
\]

Next, we calculate \( 60 \times 13 \):

\[
60 \times 13 = 780
\]

Now, we can substitute this back into the volume equation:

\[
V = \frac{1}{3} \times 780
\]

To calculate \( \frac{1}{3} \times 780 \):

\[
V = 260
\]

Thus, the volume of the triangular pyramid is:

\[
\text{Volume} = 260 \text{ cubic inches}
\]

The correct answer is \( \boxed{260} \text{ in}^3 \).