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

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

The total cost $C(x)$ in Rupees associated with the production of $x$ units of an item is given by $C(x) = 0.007x^{3} - 0.003x^{2} + 15x + 4000$. Find the marginal cost when $17$ units are produced.

The rate of change of the area of a circle with respect to its radius at $r = 3 \text{ cm}$ is . . . . . . $\text{cm}^2/\text{cm}$. (in $\pi$)

The distance $s$ in meters travelled by a particle in $t$ seconds is given by $s = \frac{2 t^3}{3} - 18 t + \frac{5}{3}$. The acceleration when the particle comes to rest is (in $m/s^2$)

The radius of a circular plate is increasing at the rate of $0.01 \text{ cm/sec}$. When the radius is $12 \text{ cm}$,the rate at which the area increases is: