
The side of a square sheet of a metal is increasing at a rate of centimetres per minute. At what rate is the area increasing in when the side is long?

Important Questions on Applications of Derivatives
The radius of a spherical soap bubble is increasing at the rate of . If the rate of increase of its surface area when the radius is is , then find the value of . (Take )
{Write the answer in decimal form}

The radius of an air bubble is increasing at the rate of centimetre per second. At what rate is the volume of the bubble increasing in when the radius is centimetre? (Take )

The volume of a spherical balloon is increasing at the rate ofcubic centimetres per second. Find the rate of change of its surface in at the instant when its radius is .


The bottom of a rectangular swimming tank is by . Water is pumped into the tank at the rate of cubic metres per minute. Find the rate at which the level of water in the tank is rising in .


A tall man walks at a uniform speed of away from a high lamp post. Find the rate at which the length of his shadow increases in .

An inverted cone has a depth of and a base of radius . Water is poured into it at a rate of cubic centimetres per minute. The rate at which the level of water in the cone is rising when the depth is in is , where and are smallest positive integers . Find. (Take )
