+48 a cylinder and a cone have the same height, but the base radius of the cylinder is only half of that cone. If the volume of the cylinder is 1, then what is the volume of the cone?
+128474 Let h = the height of both
Let the radius of the cylinder = R and that of the cone = 2R
So for the cylinder
1 = pi * R^2 * h
And for the cone
V = (1/3) pi ( 2R)^2 *h = (1/3)pi * (4 R^2) * h = (4/3) pi R^2 *h
But
pi R^2 * h = 1
So....the volume of the cone =
(4/3) (1) = 4/3
