# Thread: Right Circular Cone

1. ## Right Circular Cone

Water is poured into a container in the shape of a right circular cone with radius 4 feet and a height of 16 feet. Express the volume V of the water in the cone as a function of the height h of the water.

HINT GIVEN:

The volume V of a cone of radius r and height h is V = (1/3)(pi)(r^2)(h).

NOTE: Since the radius is 4 feet, does it mean the diameter of the cone is 8 feet?

2. Originally Posted by symmetry
Water is poured into a container in the shape of a right circular cone with radius 4 feet and a height of 16 feet. Express the volume V of the water in the cone as a function of the height h of the water.

HINT GIVEN:

The volume V of a cone of radius r and height h is V = (1/3)(pi)(r^2)(h).
As the radius of the cone is 4 ft, and height is 16 ft, when the cone is filled
to a height of h ft, the radius of the surface of the liquid is h/4 ft (as the
filled part of the cone is similar to the whole cone the radius to height ratio
is the same as that for the whole cone). So r=h/4, hence the volume:

V=(1/3) pi r^2 h = (1/3) pi (h/4)^2 h= (1/48) pi h^3.

NOTE: Since the radius is 4 feet, does it mean the diameter of the cone is 8 feet?
yes

RonL

3. ## ok

I get it now thanks to you.

Thanks!