The diameter of one of the bases of a truncated cone is $100 \, mm$. If the diameter of this base is increased by $21 \%$ such that it still remains a truncated cone with the height and the other base unchanged,the volume also increases by $21 \%$. The radius of the other base (in $mm$) is

The total cost $C(x)$ in Rupees,associated with the production of $x$ units of an item is given by $C(x) = 0.005x^{3} - 0.02x^{2} + 30x + 5000$. Find the marginal cost when $3$ units are produced,where marginal cost is defined as the instantaneous rate of change of total cost with respect to the number of units produced.

$A$ balloon starting from rest is ascending from the ground with a uniform acceleration of $4 \ ft/sec^2$. At the end of $5 \ sec$,a stone is dropped from it. If $T$ is the time taken for the stone to reach the ground and $H$ is the height of the balloon when the stone reaches the ground,then:

If the radius of a circle increases at the rate of $7 \text{ cm/sec}$,then the rate of increase of its area after $10 \text{ minutes}$ is:

The displacement $s$ of a particle,in meters,at any time $t$ in seconds is expressed as $s = \frac{t^3}{3} - 6t$. Find the acceleration at the time when the velocity vanishes.

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?