Determine the volume of a rectangular pyramid that has a height of 18 inches and a base area of 160 inches.
Understand the Problem
The question asks to calculate the volume of a rectangular pyramid given its height and base area. The formula for the volume of a pyramid is (1/3) * base area * height. We are given the height as 18 inches and the base area as 160 inches.
Answer
$V = 960$ cubic inches
Answer for screen readers
$V = 960$ cubic inches
Steps to Solve
- Write the formula for the volume of a pyramid
The volume $V$ of a pyramid is given by: $$ V = \frac{1}{3} \times B \times h $$ where $B$ is the area of the base and $h$ is the height of the pyramid.
- Substitute the given values into the formula
We are given that the base area $B = 160$ square inches and the height $h = 18$ inches. Substituting these values into the formula: $$ V = \frac{1}{3} \times 160 \times 18$$
- Calculate the volume $$ V = \frac{1}{3} \times 160 \times 18 = \frac{2880}{3} = 960 $$
Therefore, the volume of the rectangular pyramid is 960 cubic inches.
$V = 960$ cubic inches
More Information
The unit of volume is cubic inches because we are multiplying area (square inches) by length (inches).
Tips
A common mistake is forgetting to multiply by $\frac{1}{3}$ in the formula for the volume of a pyramid. Another mistake is using the incorrect units, for example, using square inches instead of cubic inches for volume.
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