Question

Two similar pipes are shown.



The small pipe has a radius of 10 feet and a height of 22 feet while the large pipe has a height of 33 feet. What is the volume of the large pipe in terms of π?
Answer
2,200π ft3
2,475π ft3
4,500π ft3
7,425π ft3

Answer 1

The volume of the smaller pipe is: pi * 10*10 * 22 = 2200 pi.
The larger pipe is similar to the smaller one and the scale factor from small to large is 22 to 33 which simplifies to 2 to 3 or 2/3.
If two solids are similar the cube of the scale factor is the ratio of the volumes.
(2/3) ^3 = 2200 pi / V where V is the volume of the larger solid
8/27 = 2200 pi / V
V = (27 * 2 200 pi) / 8 = 7 425 pi --> ANS