Question

A block of ice in the shape of a right circular cone is melting in such a way that both its height and its radius r are decreasing at the rate of 1 cm/hr. How fast is the volume decreasing when r = h = 10 cm?

Answer 1

The volume of the cone is decreasing at a rate of ___ cm³/hr.

Step-by-step explanation:

Given that both the height and radius of the ice cone are decreasing at a rate of 1 cm/hr, we can use the formula for the volume of a cone to find the rate at which the volume is decreasing.

The volume of a cone is given by the formula V = (1/3)πr^2h. Taking the derivative with respect to time, we get dV/dt = (1/3)π(r^2(dh/dt) + h(2r(dr/dt))).

When r = h = 10 cm, the rate at which the volume is decreasing can be calculated by substituting the values into the derivative expression and solving for dV/dt.