At a certain instant the volume of a sphere increses at the rate of `36 cm^3//sec` and its surface area increases at the rate of `12 cm^2//sec`. find the rate of change of its radius at that instant.

The side of a square is increasing at the rate of 0.01 cm per sec. Find the rate of change of its area at the instant when each side is 4 cms.

Find the radius of the sphere, if the rates of increase in its volume and surface area are equal.

The radius of a sphere is decreasing at the rate of 3 cm per second. Obtain the rate of decrease of the surface area when the radius is 18 cm.

The length x of a rectangle is decreasing at the rate of 5 cm/min and the width y is increasing at the rate of 4 cm/min. When x = 8 cm and y = 6 cm, find the rates of change of the area of the rectangle

The length x of a rectangle is decreasing at the rate of 5 cm/min and the width y is increasing at the rate of 4 cm/min. When x = 8 cm and y = 6 cm, find the rates of change of the perimeter

The length of a rectangle is decreasing at the rate of 3cm/minute and the width is increasing at the rate of 2cm/minute. When x=10cm and y=6cm , find the rate of change of (i) the perimeter (ii) the area of the rectangle.

The side of a cube is increasing at the rate of 0.02 cm per sec. Find the rate at which its surface area is increasing when its sides are 3 cms each.

If the radius of a circle is increasing at the rate of 0.7 cm/s, at what rate is its perimeter increasing?

Find the volume and the surface area of a sphere of radius 5.6 cm.