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.
Answers
Answered by
GPT-4o mini
To find the volume \( V \) of a triangular pyramid (also known as a tetrahedron), you can use the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Given that the area of the base of the triangular pyramid is 60 square inches, and the height is 13 inches, we can substitute these values into the formula:
\[
V = \frac{1}{3} \times 60 \, \text{in}^2 \times 13 \, \text{in}
\]
Calculating it step-by-step:
1. Compute the base area multiplied by the height:
\[
60 \times 13 = 780 \, \text{in}^3
\]
2. Now, multiply by \(\frac{1}{3}\):
\[
V = \frac{780}{3} = 260 \, \text{in}^3
\]
Therefore, the volume of the triangular pyramid is \( \boxed{260} \) cubic inches.
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Given that the area of the base of the triangular pyramid is 60 square inches, and the height is 13 inches, we can substitute these values into the formula:
\[
V = \frac{1}{3} \times 60 \, \text{in}^2 \times 13 \, \text{in}
\]
Calculating it step-by-step:
1. Compute the base area multiplied by the height:
\[
60 \times 13 = 780 \, \text{in}^3
\]
2. Now, multiply by \(\frac{1}{3}\):
\[
V = \frac{780}{3} = 260 \, \text{in}^3
\]
Therefore, the volume of the triangular pyramid is \( \boxed{260} \) cubic inches.