Given that the area of a circular disk is increasing at a rate of and , determine the rate of increase of its radius when the radius is cm.
Given that the area of a circular disk is increasing at a rate of , and , determine the rate of increase of its radius when it is cm.
The formula for the area, , of a circle is , where is the circle's radius.
First, consider to be a function of , and to be a function of , or the time in seconds. Then use implicit differentiation to find the formula's derivative as follows:
Now, since the area of the circular disk was increasing at a rate of square centimetres per second when the disk's radius was 18 centimetres, substitute for and 18 for in the equation , and solve for , using for .
Thus, the rate of increase of the disk's radius when the radius was 18 centimetres was centimetres per second.