Question

the radius of a sphere increases at a rate of 1 m/sec. find the rate at which the volume increases when the radius is 20 m.

Answer 1

To find the rate at which the volume of a sphere increases when the radius increases by 1 m/sec, we can differentiate the formula for the volume of a sphere and substitute the given values to calculate the rate of change.

Step-by-step explanation:

To find the rate at which the volume of a sphere increases when the radius increases by 1 m/sec, we can use the formula for the volume of a sphere: V = (4/3)πr³, where V is the volume and r is the radius.

First, we can differentiate both sides of the equation with respect to time to find the rate of change of the volume with respect to time: dV/dt = 4πr²(dr/dt).

Since we know that dr/dt = 1 m/sec, and we want to find dV/dt when r = 20 m, we can substitute these values into the equation to find the rate at which the volume increases.