Cecilia built a model pyramid out of foam.

Her model is 20 inches high, with a rectangular base that is 8 inches long and 12 inches wide. What is the volume of her model in cubic inches?

1 answer

To find the volume of the pyramid, you can use the formula for the volume of a rectangular pyramid:

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

The base area of a rectangle is calculated by multiplying the length and width. In this case, the length of the base is 8 inches and the width is 12 inches:

\[ \text{Base Area} = \text{Length} \times \text{Width} = 8 , \text{inches} \times 12 , \text{inches} = 96 , \text{square inches} \]

Now we can use the base area and the height (20 inches) in the volume formula:

\[ V = \frac{1}{3} \times 96 , \text{square inches} \times 20 , \text{inches} \]

Calculating this step-by-step, we first find the product of the base area and height:

\[ 96 , \text{square inches} \times 20 , \text{inches} = 1920 , \text{cubic inches} \]

Now, we apply the \(\frac{1}{3}\) factor:

\[ V = \frac{1}{3} \times 1920 , \text{cubic inches} = 640 , \text{cubic inches} \]

Thus, the volume of Cecilia's model pyramid is

\[ \boxed{640} , \text{cubic inches} \]