a cylinder has a radius of 10 and height of 4.
if the cylinder and The Cone have the same volume then what would be the height and radius of the cone
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
Given that the cylinder has a radius of 10 and a height of 4, the volume of the cylinder is V_cylinder = π(10^2)(4) = 400π.
For a cone, the volume is given by the formula V_cone = (1/3)πr^2h, where r is the radius and h is the height.
Since the volumes of the cylinder and cone are the same, we have:
400π = (1/3)πr^2h.
Substitute the values of the cylinder's dimensions:
400π = (1/3)π(10)^2h.
Solving for h, we get h = (400π) / ((1/3)π(100))
h = 12
Therefore, the height of the cone is 12.
Substitute the value of the height back into the equation:
400π = (1/3)πr^2(12).
r^2 = (400π) / ((1/3)π12)
r^2 = 100
r = 10
Therefore, the radius of the cone is 10.