Question

The base of a rectangular pyramid has sides 3 feet long and 7 feet long. The pyramid is 4 feet tall. A second, larger pyramid has dimensions that are 3 times the dimensions of the smaller pyramid. What is the difference between the volumes of the two pyramids?

Answer 1

728 is the difference between the two areas.

Answer 2

The difference between the volumes is 728 ft³.

Explanation:

Our first step will be to find the volume of the smaller pyramid. Notice that we have all the necessary dimensions. The formula for the volume of a pyramid is

`V = (A_bh)/(3),`

where
`h` stands for the height and
`A_b` for the area of the basis. In this case
`h=4 ft`, and the area of the basis, which is a rectangle, is
`A_b = 3 ft * 7 ft = 21 ft².` Then,

`V = ((21 ft²)(4 ft))/(3) = 28 ft³.`

Now, two calculate the volume of the second pyramid, recall that it has dimensions three times larger. This means,
`h=3*4 ft=12 ft` and
`A_b = (3*3 ft) *(3* 7 ft) = 9*21 ft² = 189 ft².` Then,

`V = ((189 ft²)(12 ft))/(3) = 756 ft³.`

Finally, we only need to substract the values of the volumes:

756 ft³-28 ft³= 728 ft³.