Question

Cone S and cone T are similar. The volume of cone S is 768 768pi cm3 cm3 and the

volume of cone T is 6144 6144pi cm3 cm3. What is the height of cone S if the height
of cone Tis 24 cm?
24 cm
cone S
cone T

Answer 1

Explanation:

This is a ratio problem

Vol cone = 1/3 π r² h

Cone S is 768pi cm3

Cone T is 6144pi cm3

Cone S and cone T are similar I think this means they have the same radius

Vol cone S = 1/3 π r² hs Vol cone T = 1/3 π r² ht

Vol Cone S / Vol Cone T = 1/3 π r² hs / 1/3 π r² ht

Vol Cone S / Vol Cone T = hs / ht

768 / 6144 = hs / 24 (note the π cancelled out

h cone s = 768(24) / 6144

h cone s = 3 cm