Question

1 point

The volume of a container varies jointly with the square of its radius, r, and its height, h. The
container has a height of 10 centimeters, and radius of 6 centimeters, and a volume of 377 cubic
centimeters. What is the volume of a container with a radius of 4 centimeters and a height of 4
centimeters?
Your answer

Answer 1

The volume of a container with a radius of 4 centimeters and a height of 4 centimeters is 67.2 cubic centimeter

Solution:

The volume of a container varies jointly with the square of its radius, r, and its height, h

Therefore,

`v \propto r^2 h\\\\v = k * r^2h -------- eqn\ 1`

The container has a height of 10 centimeters, and radius of 6 centimeters, and a volume of 377 cubic centimeters

Substitute v = 377 and h = 10 and r = 6 in eqn 1

`377 = k * 6^2 * 10\\\\377 = k * 360\\\\k = 1.047 \approx 1.05`

What is the volume of a container with a radius of 4 centimeters and a height of 4 centimeters?

Substitute k = 1.05 and r = 4 and h = 4 in eqn 1

`v = 1.05 * 4^2 * 4\\\\v = 1.05 * 16 * 4\\\\v = 67.2`

Thus volume of a container with a radius of 4 centimeters and a height of 4 centimeters is 67.2 cubic centimeter