Describe what happens to the volume of a cone when the radius is doubled while its height is halved. The volume is

The volume of a cone is given by the formula V = 1/3πr²h, where r is the radius and h is the height.

If the radius is doubled, the new radius is 2r. If the height is halved, the new height is h/2.

Substituting these values into the formula gives the new volume as V' = 1/3π(2r)²(h/2).

Simplifying this gives V' = 1/3π4r²h/2 = 2/3πr²h.

Comparing this with the original volume, we see that the new volume is twice the original volume. Therefore, when the radius of a cone is doubled and its height is halved, the volume of the cone doubles.

The volume of a cone is given by the formula V = 1/3πr²h, where r is the radius and h is the height.

If the radius is doubled, the new radius will be 2r. If the height is halved, the new height will be h/2.

Substituting these values into the formula gives us the new volume V' = 1/3π(2r)²(h/2).

Simplifying this gives V' = 1/3π4r²h/2 = 2/3πr²h.

Comparing this with the original volume, we see that the new volume is twice the original volume. Therefore, when the radius of a cone is doubled and its height is halved, the volume of the cone doubles.