The surface area of a spherical balloon is increasing at the rate of $2 \text{ cm}^2/\text{sec}$. Find the rate of increase in the volume of the balloon when the radius of the balloon is $6 \text{ cm}$.

$A$ water tank has the shape of an inverted right circular cone,whose semi-vertical angle is $\tan^{-1}(1/2)$. Water is poured in at a constant rate of $5 \ m^3/min$. Then the rate (in $m/min$) at which the level of water is rising at the instant when the depth of water in the tank is $10 \ m$ is:

In $\Delta ABC$,sides $a$ and $b$ are kept constant such that there is an error $\alpha$ in angle $C$. What is the relative error in the area?

$OA$ and $OB$ are two roads enclosing an angle of $120^{\circ}$. $X$ and $Y$ start from '$O$' at the same time. $X$ travels along $OA$ with a speed of $4 \text{ km/h}$ and $Y$ travels along $OB$ with a speed of $3 \text{ km/h}$. The rate at which the shortest distance between $X$ and $Y$ is increasing after $1 \text{ h}$ is

The distance $s$ (in meters) covered by a particle in $t$ seconds is given by $s = ae^t + \frac{b}{e^t}$. Then the acceleration of the particle at time $t$ is:

If a circular iron sheet of radius $30 \, cm$ is heated such that its area increases at the uniform rate of $6\pi \, cm^2/hr$,then the rate (in $cm/hr$) at which the radius of the circular sheet increases is