If the radius $r$ of a sphere is increasing at a rate of $2 \text{ cm/s}$,then the rate of change of its surface area is proportional to which of the following?

If the volume of a sphere increases at the rate of $2 \pi \text{ cm}^3/\text{s}$,then the rate of increase of its radius (in $\text{cm}/\text{s}$),when the volume is $288 \pi \text{ cm}^3$,is

The height of a right circular cylinder is decreasing while its diameter is increasing at a rate of $4 \text{ cm/s}$ so as to keep its volume unchanged. The rate of change in its lateral surface area (in $\text{cm}^2/\text{s}$) at the instant when its diameter is $8 \text{ cm}$ and height is $12 \text{ cm}$, is (in $\pi$)

Water is running into a hemispherical bowl of radius $180 \text{ cm}$ at the rate of $108 \text{ dm}^3/\text{min}$. How fast is the water level rising when the depth of the water in the bowl is $120 \text{ cm}$? $(1 \text{ dm} = 10 \text{ cm})$

$A$ ladder $20 \ ft$ long leans against a vertical wall. The top end slides downwards at the rate of $2 \ ft/sec$. The rate at which the lower end moves on a horizontal floor when it is $12 \ ft$ from the wall is

If the edge of a cube increases at the rate of $60 \, cm/s$,at what rate is the volume increasing when the edge is $90 \, cm$ (in $cm^3/s$)?