Question

What is the height of cone S?

Answer 1

(Set up a proportion: 768pi/6144pi = x/24)
(Cross multiply: 6144pi*x = 18432pi)
(Divide both sides by 6144pi: x = 3)
(The height of cone S = 3 cm)

Answer 2

Answer:

12 cm

Step-by-step explanation:

First, we find the scale factor from cone S to cone T.

ratio of volumes = (vol of T)/(vol of S) = (6144 pi cm^3)/(768 pi cm^3) = 8

The ratio of the volumes is 8:1

The scale factor, which is the ratio of linear dimensions (height, radius, etc.), is the cubic root of the ratio of the volumes.

scale factor = cubic root of 8 = 2

The height of cube T is 24 cm, so the height of cube S is 24 cm/2 = 12 cm.