Question

the cylinder had a radius of 10 and a height of 4. if a cone had the same volume of the cylinder what would the radius and height of the cone be

Answer 1

First, we need to find the volume of the cylinder:

Volume of cylinder = π(radius)^2(height)
Volume of cylinder = π(10)^2(4)
Volume of cylinder = π(100)(4)
Volume of cylinder = 400π

Now, we need to find the volume of the cone:

Volume of cone = 1/3 * π(radius)^2(height)

Since the volume of the cone is equal to the volume of the cylinder:
400π = 1/3 * π(radius)^2(height)

Simplify the equation:
1200 = (radius)^2(height)

Given that the radius of the cylinder is 10 and the height is 4:
1200 = (10)^2(4)
1200 = 100(4)
1200 = 400

So, the cone has a radius of 10 and a height of 3 in order to have the same volume as the cylinder.