Question

The solid below is dilated by a scale factor of 1/2. 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 number 3.

Answer 1

Corrected solution (final answer in terms of π):

1) Volume of preimage (cylinder): V = πr^2h = π(10)^2(6) = 600π.

2) Scale factor k = 1/2. Volume scales by k^3, so
V' = V·k^3 = 600π·(1/2)^3 = 600π·(1/8) = 75π.

Answer: 75π units^3.

Note: the earlier work incorrectly used (1/4)^3 = 1/64; the correct factor is (1/2)^3 = 1/8.