The surface area of a spherical bubble increases at a rate of $2 \text{ cm}^2/\text{s}$. The rate at which the volume of the bubble increases when the radius is $6 \text{ cm}$ is . . . . . . $\text{cm}^3/\text{s}$.

$A$ swimming pool is to be drained for cleaning. If $L$ represents the number of litres of water in the pool $t$ seconds after the pool has been plugged off to drain and $L=200(10-t)^{2}$,how fast is the water running out at the end of $5$ seconds? What is the average rate at which the water flows out during the first $5$ seconds?

Each edge of a cube is expanding at the rate of $1 \text{ cm/sec}$. Then the rate (in $\text{cc/sec}$) of change in its volume,when each of its edge is of length $5 \text{ cm}$,is

The rate of change of the area of a circle with respect to its radius $r$ at $r = 6 \text{ cm}$ is

$A$ particle starts moving from rest from a fixed point in a fixed direction. The distance $s$ from the fixed point at a time $t$ is given by $s = t^{2} + at - b + 17$, where $a$ and $b$ are real numbers. If the particle comes to rest after $5 \ s$ at a distance of $s = 25$ units from the fixed point, then the values of $a$ and $b$ are respectively:

$A$ spherical iron ball of radius $10 \, cm$ is coated with a layer of ice of uniform thickness that melts at a rate of $50 \, cm^3/min$. When the thickness of the ice is $5 \, cm$,find the rate at which the thickness of the ice decreases.