Question

A triangular pyramid with a height of 9 inches has a volume of 63 cubic inches. If the height of the triangular base is 6 inches,
what is the base length of the triangular base? (Recall the formula V - 3 Bh)
A) 2 2/3 in
B) 7 in
C) 10 1/2 in
D) 21 in

Answer 1

Option D: 21 in is the base length of the triangular base.

Explanation:

Given that a triangular pyramid with a height of 9 inches has a volume of 63 cubic inches.

The height of the triangular base is 6 inches.

We need to determine the base length of the triangular pyramid.

The base length of the triangular pyramid can be determined using the formula,

$Volume =\frac{1}{3} \times Bh$

Substituting $Volume=63$ and $Height=9$ in the above formula, we get,

$63 =\frac{1}{3} \times B(9)$

Simplifying the terms, we get,

$63 =3B$

Dividing both sides by 3, we have,

$21=B$

Thus, the base length of the triangular pyramid is 21 in

Hence, Option D is the correct answer.