Question

The solid below is dilated by a scale factor of one half
2
1
​
. Find the volume of the solid created upon dilation. Answer in terms of piπ.
6

units, cubed units
3

_______ units to the power of 3

Answer 1

Scale factor k = 1/2, so volumes scale by k^3 = (1/2)^3 = 1/8.

If the original solid is a cylinder with radius 3 and height 6, its volume is
V = πr^2h = π(3^2)(6) = 54π.

After dilation V' = (1/8)·54π = 54π/8 = 27π/4.

Answer: 27π/4 cubic units.