Question

Three cones have a volume of 192 cm³. Cone A has a radius of 2 cm. Cone B has a

radius of 3 cm. Cone C has a radius of 4 cm. Find the height of each cone.

Answer 1

A: 144 cm

B: 64 cm

C: 36 cm

Explanation:

The volume of a cone is given by ...

V = (1/3)πr²h

Solving for h, we get ...

3V/(πr²) = h

Filling in the given values, we get ...

3(192π)/(πr²) = h

576/r² = h

Then the heights of the different cones are ...

A: r = 2, h = 576/4 = 144 . . . cm

B: r = 3, h = 576/9 = 64 . . . cm

C: r = 4, h = 576/16 = 36 . . . cm