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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?

User Gizel
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2 Answers

5 votes
728 is the difference between the two areas.
User Dan Kendall
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7 votes

Answer:

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.

User Ben Romberg
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