Question

A cylinder and a cone have the same volume. The cylinder has radius x and height y. The cone has radius 2x. Find the height of the cone in terms of y.

Answer 1

I'm pretty sure the height is 3/4y.

Answer 2

The volume of the cone is (x)(x)(y)(pi)

That is equal to the volume of the cone, or 1/3{2x(2x)(height)(pi)}

Set the, equal to each other.

x(x)y(pi)=1/3{2x(2x)(height)(pi)}

Divide pi out from both sides.

x(x)y=1/3{2x(2x)(height)}

Divide X out.

xy=1/3{2(2x)height}

Divide X out again.

y=1/3{4(height)}

Multiply both sides by 3.

3y=4(height)

Since we want the height, isolate it.

3/4y=height

The height of the cone is 3/4y.

Hope this helps!