The rate of change of the area of a sphere with respect to its radius, when the radius is $6 \text{ cm}$, is . . . . . . . (in $\pi$)

An ice layer of uniform thickness is deposited on an iron sphere of radius $10 \text{ cm}$. The ice melts at a rate of $50 \text{ cm}^3/\text{min}$. When the thickness of the ice layer is $5 \text{ cm}$,the rate at which the thickness of the ice layer is decreasing is ...... $\text{cm/min}$.

The radius of a right circular cylinder increases at the rate of $0.1 \text{ cm/min}$ and the height decreases at the rate of $0.2 \text{ cm/min}$. The rate of change of the volume of the cylinder in $\text{cm}^3\text{/min}$,when the radius is $2 \text{ cm}$ and the height is $3 \text{ cm}$,is:

$A$ stone is dropped into a quiet lake and waves move in circles at the speed of $ 5 \text{ cm s}^{-1} $. At that instant,when the radius of the circular wave is $ 8 \text{ cm} $,how fast is the enclosed area increasing?

The sides of an equilateral triangle are increasing at the rate of $2 \text{ cm/sec}$. The rate at which the area increases,when the side is $10 \text{ cm}$,is

The rate of change of the volume of a sphere with respect to its surface area,when its radius is $2 \text{ cm}$,is . . . . . . $\text{cm}^3 / \text{cm}^2$.