Question
The area of the base of a triangular pyramid is 75 square inches. The height of the pyramid is 14 inches.
What is the volume of the triangular pyramid in cubic inches?
What is the volume of the triangular pyramid in cubic inches?
Answers
GPT-4o mini
The volume \( V \) of a triangular pyramid (or tetrahedron) can be calculated using the formula:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
In this case, we know the area of the base is 75 square inches, and the height of the pyramid is 14 inches. We can substitute these values into the formula:
\[
V = \frac{1}{3} \times 75 \, \text{in}^2 \times 14 \, \text{in}
\]
Calculating the product of the base area and the height:
\[
75 \times 14 = 1050
\]
Now substitute this back into the volume formula:
\[
V = \frac{1}{3} \times 1050
\]
Calculating the volume:
\[
V = 350 \, \text{in}^3
\]
Therefore, the volume of the triangular pyramid is
\[
\boxed{350} \, \text{cubic inches}.
\]
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]
In this case, we know the area of the base is 75 square inches, and the height of the pyramid is 14 inches. We can substitute these values into the formula:
\[
V = \frac{1}{3} \times 75 \, \text{in}^2 \times 14 \, \text{in}
\]
Calculating the product of the base area and the height:
\[
75 \times 14 = 1050
\]
Now substitute this back into the volume formula:
\[
V = \frac{1}{3} \times 1050
\]
Calculating the volume:
\[
V = 350 \, \text{in}^3
\]
Therefore, the volume of the triangular pyramid is
\[
\boxed{350} \, \text{cubic inches}.
\]