The radius of a sphere is measured to be $20 \, cm$ with a possible error of $0.02 \, cm$. The consequent error in the surface area of the sphere is ....... $sq \, cm$.

$A$ closed conical vessel is filled with water fully and is placed with its vertex down. The water is let out at a constant speed. After $21 \, min$,it was found that the height of the water column is half of the original height. How much more time in minutes does it require to empty the vessel?

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

$A$ man of height $2 \ m$ walks at a uniform speed of $5 \ km/hr$ away from a lamp post which is $6 \ m$ high. Find the rate at which the length of his shadow increases in $km/hr$.

The volume of a spherical balloon is increasing at the rate of $2 \ cm^3/sec$. When its radius is $4 \ cm$, the rate of change of its surface area (in $cm^2/sec$) 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.