Volume of Pyramids Practice

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Question
Use the image to answer the question.

An illustration shows a rectangular pyramid with a length of 8 millimeters, a width of 5 millimeters, and a perpendicular height of 18 millimeters. The right and front faces are visible. Edges and faces that are not visible are indicated by dashed lines.

What is the volume of the rectangular pyramid?

(1 point)
mm3

1 answer

The volume \( V \) of a rectangular pyramid can be calculated using the formula:

\[ V = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

For a rectangular base, the area \( \text{Base Area} \) can be calculated as:

\[ \text{Base Area} = \text{Length} \times \text{Width} \]

Given the dimensions:

  • Length = 8 mm
  • Width = 5 mm
  • Height = 18 mm

First, calculate the area of the base:

\[ \text{Base Area} = 8 , \text{mm} \times 5 , \text{mm} = 40 , \text{mm}^2 \]

Next, plug the base area and height into the volume formula:

\[ V = \frac{1}{3} \times 40 , \text{mm}^2 \times 18 , \text{mm} \]

Calculating this gives:

\[ V = \frac{1}{3} \times 720 , \text{mm}^3 = 240 , \text{mm}^3 \]

Thus, the volume of the rectangular pyramid is:

\[ \boxed{240} , \text{mm}^3 \]