Question

The solid below is dilated by a scale factor of 1/4. Find the volume of the solid created upon dilation. Answer in terms of π. Make a different version of Volume of preimage=
πr
2
h
Formula for volume of a cylinder
equals, pi, dot, 10, squared, dot, 6
=
π⋅10
2
⋅6
Substitute
equals, 600, pi, units, cubed
=
600π units
3

Volume after dilation, equals, Volume of preimage, dot, k, cubed
Volume after dilation=
Volume of preimage⋅k
3

Volume has three dimensions, so we scale by k, cubedk
3

equals, 600, pi, dot, left parenthesis, one quarter, right parenthesis, cubed
=
600π⋅(
4
1
​
)
3

Substitute
equals, 600, pi, dot, start fraction, 1, divided by, 64, end fraction
=
600π⋅
64
1
​

Exponents
equals, 9, point, 3, 7, 5, pi, units, cubed
=
9.375π units
3 but with the numbers 10, 10, and 10.

Answer 1

Volume of preimage:
V = πr^2h = π(10^2)(10) = π·100·10 = 1000π units^3

Scale factor k = 1/4. Volume scales by k^3:
V' = V·k^3 = 1000π·(1/4)^3 = 1000π·(1/64) = (1000/64)π = 125/8 π units^3

(Decimal form: 15.625π units^3.)