Question

the formula for the volume of a pyramid is $v = \frac{1}{3}bh$, where $b$ is the area of the base of the pyramid and $h$ is the height of the pyramid. what is the volume of this pyramid in cubic inches? image of a pyramid with height 8 in, and base triangle with base 6 in and height 5 in

Explanation:

Step1: Find the area of the base (B)

The base of the pyramid is a triangle. The formula for the area of a triangle is \( B=\frac{1}{2}\times base\times height \). From the diagram, the base of the triangular base is 6 in and the height of the triangular base is 5 in. So, \( B = \frac{1}{2}\times6\times5 \).
\( B=\frac{1}{2}\times30 = 15 \) square inches.

Step2: Identify the height (h) of the pyramid

From the diagram, the height \( h \) of the pyramid is 8 in.

Step3: Calculate the volume (V) of the pyramid

The formula for the volume of a pyramid is \( V=\frac{1}{3}Bh \). We know \( B = 15 \) and \( h = 8 \), so substitute these values into the formula: \( V=\frac{1}{3}\times15\times8 \).
First, \( \frac{1}{3}\times15 = 5 \), then \( 5\times8 = 40 \).

Answer:

40