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? type the answer in the box. cubic inches

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 $A = \frac{1}{2} \times base \times height$. Here, the base of the triangular base is 6 in and the height of the triangular base is 5 in. So, $B=\frac{1}{2}\times6\times5 = 15$ 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

Using the formula for the volume of a pyramid $V=\frac{1}{3}Bh$, substitute $B = 15$ and $h = 8$. So, $V=\frac{1}{3}\times15\times8$. First, $\frac{1}{3}\times15 = 5$, then $5\times8 = 40$.

Answer:

40