Question
the area of the base of a triangular pyramid is 60 square inches. the height of the pyramid is 13 in
what is the volume of the triangular pyramid in cubic inches?
a. 390 in cubed
b. 260 in cubed
c. 780 in cubed
d. 130 in cubed
what is the volume of the triangular pyramid in cubic inches?
a. 390 in cubed
b. 260 in cubed
c. 780 in cubed
d. 130 in cubed
Answers
Answered by
GPT-4o mini
To find the volume of a triangular pyramid (also known as a tetrahedron), you can use the formula:
\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Given:
- Base Area = 60 square inches
- Height = 13 inches
Plugging these values into the formula:
\[
\text{Volume} = \frac{1}{3} \times 60 \, \text{in}^2 \times 13 \, \text{in}
\]
Calculating:
\[
\text{Volume} = \frac{1}{3} \times 780 \, \text{in}^3 = 260 \, \text{in}^3
\]
Therefore, the volume of the triangular pyramid is \( 260 \) cubic inches, which corresponds to option **b**.
\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
Given:
- Base Area = 60 square inches
- Height = 13 inches
Plugging these values into the formula:
\[
\text{Volume} = \frac{1}{3} \times 60 \, \text{in}^2 \times 13 \, \text{in}
\]
Calculating:
\[
\text{Volume} = \frac{1}{3} \times 780 \, \text{in}^3 = 260 \, \text{in}^3
\]
Therefore, the volume of the triangular pyramid is \( 260 \) cubic inches, which corresponds to option **b**.