A spherical rain drop evaporates at a rate proportioanl to its surface area. Form a differntial equation involving the rate of change of the radius of the rain drop.

Spherical rain drop evaporates at a rate proportional to its surface area. The differential equation corresponding to the rate of change of the radius of the rain drop if the constant of proportionality is K gt 0 is

A right circular cone with radius R and height H contains a liquid which evaporates at a rate proportional to its surface area in contact with air (proportionality constant =k gt 0 ). Find the time after which the cone will be empty.

Find the rate of the change of surface area of a sphere when its radius is increasing at the rate of 3/pi cm/min and its radius is 1 cm.

The length of a rectangle is increasing at the rate of 3.5 cm/sec and its breadth is decreasing at the rate of 3cm/sec. Find the rate of change of the area of the rectangle when length is 12 cm and breadth is 8 cm.

In a competition, a brave child tries to inflate a huge spherical balloon bearing slogans against child labour at the rate of 900 cubic centimeter of gas per second. Find the rate at which the radius of the balloon is increasing when its radius is 15 cm. Also write any three value/life skill reflected in this question.

The radius of a spherical soap bubble is increasing at the rate of 0.5 cm per second. Find the rate of change of its volume, when the radius is 10 cm.