Question

The solid below is dilated by a scale factor of 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 4 and 4.

Answer 1

Use r = 4 and h = 4.

Volume of preimage:
V0 = πr^2h = π·4^2·4 = π·16·4 = 64π units^3

Scale factor k = 4, so volume scales by k^3 = 4^3 = 64.

Volume after dilation:
V = V0·k^3 = 64π·64 = 4096π units^3