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 point)

in3

1 answer

To find the volume of a pyramid, the formula is given by:

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

First, we need to calculate the base area of the pyramid. The base is a rectangle with length \( L = 8 \) inches and width \( W = 12 \) inches. The area of the base can be calculated as:

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

Now we can plug the base area and the height \( H = 20 \) inches into the volume formula:

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

Calculating this step-by-step:

  1. Multiply the base area by the height:

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

  1. Now divide by 3:

\[ \text{Volume} = \frac{1920}{3} = 640 , \text{cubic inches} \]

Thus, the volume of Cecilia's model pyramid is

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