a cylinder has a radius of 10 and height of 4.
if the cylinder and The Cone shown have the same volume then the radius and height of the cones should be which of these.
First, let's calculate 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
Since the volume of the cylinder and cone are equal, we can set the volume of the cone equal to 400π as well:
Volume of cone = (1/3) * π * radius^2 * height
400π = (1/3) * π * (r^2) * h
Solving for r and h, we get:
r^2 * h = (3 * 400π) / π
r^2 * h = 1200
Since we are given r=h in this scenario we can say:
r^3 = 1200
r = cube root of 1200
r ≈ 10.398
Therefore, the radius and height of the cones should be approximately 10.398 each.