The area of a triangular pyramid is 60 square inches the pyramid is 13 inches.

What is the volume of the triangular pyramid in cubic inches?
A. 390 in. squared
B. 260 in. squared
C. 780 in. squared
D. 130 in. squared

1 answer

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

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

In this case, the base area is given as 60 square inches and the height is given as 13 inches. Plugging those values into the formula:

\[ \text{Volume} = \frac{1}{3} \times 60 , \text{in}^2 \times 13 , \text{in} \]

Calculating the volume:

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

Calculating \(60 \times 13\):

\[ 60 \times 13 = 780 \]

Now divide by 3:

\[ \text{Volume} = \frac{780}{3} = 260 , \text{in}^3 \]

So the volume of the triangular pyramid is 260 cubic inches.

The correct answer is B. 260 in. squared (though it should be stated as cubic inches).