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

Answer:

The difference between the volumes is 728 ft³.

Step-by-step 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

$V = \frac{A_bh}{3},$

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,

$V = \frac{(21 ft²)(4 ft)}{3} = 28 ft³.$

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,

$V = \frac{(189 ft²)(12 ft)}{3} = 756 ft³.$

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

756 ft³-28 ft³= 728 ft³.

Answer 2

728 is the difference between the two areas.