Question

what is the volume of this rectangular pyramid?
diagram of a rectangular pyramid with height 6 mm, length 8 mm, width 6 mm
\boxed{} cubic millimeters

Explanation:

Step1: Recall the volume formula for a rectangular pyramid

The volume \( V \) of a rectangular pyramid is given by the formula \( V=\frac{1}{3} \times \text{base area} \times \text{height} \). The base of a rectangular pyramid is a rectangle, so the base area \( A \) is length \( l \) times width \( w \), i.e., \( A = l\times w \).

Step2: Identify the length, width, and height

From the diagram, the length \( l = 8 \) mm, the width \( w = 6 \) mm, and the height \( h = 6 \) mm.

Step3: Calculate the base area

First, calculate the base area. Using the formula for the area of a rectangle, \( A=l\times w \). Substituting \( l = 8 \) mm and \( w = 6 \) mm, we get \( A=8\times6 = 48 \) square millimeters.

Step4: Calculate the volume of the pyramid

Now, use the volume formula for the pyramid \( V=\frac{1}{3}\times A\times h \). We know \( A = 48 \) square millimeters and \( h = 6 \) mm. Substituting these values, we have \( V=\frac{1}{3}\times48\times6 \). First, calculate \( 48\times6=288 \), then \( \frac{1}{3}\times288 = 96 \).

Answer:

96