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
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.