Question

The radius of a right circular cone is increasing at a rate of 4.2 cm/s while its height is decreasing at a rate of 6.7 cm/s. At what rate is the volume of the cone changing when the radius is 300 cm and the height is 340 cm?

Answer 1

To find the rate at which the volume of the cone is changing, we need to use the formula for the volume of a cone and differentiate it with respect to time. Plugging in the given values, we can calculate the rate at which the volume is changing.

Step-by-step explanation:

To find the rate at which the volume of the cone is changing, we need to use the formula for the volume of a cone: V = (1/3)πr^2h. Taking the derivative of the volume function with respect to time, we get dV/dt = (1/3)π(2rh(dr/dt) + r^2(dh/dt)). Plugging in the given values, we have dr/dt = 4.2 cm/s, dh/dt = -6.7 cm/s, r = 300 cm, and h = 340 cm.

Substituting these values into the equation, we get dV/dt = (1/3)π(2(300)(340)(4.2) + (300)^2(-6.7)). Simplifying this expression will give you the rate at which the volume is changing.