The volume of a ball is increasing at the rate of $4 \pi \text{ cc/sec}$. The rate of increase of the radius,when the volume is $288 \pi \text{ cc}$,is

$A$ ladder $5 \ m$ long is leaning against a wall. The bottom of the ladder is pulled along the ground,away from the wall,at the rate of $2 \ cm/s$. How fast is its height on the wall decreasing when the foot of the ladder is $4 \ m$ away from the wall?

If a metallic circular plate of radius $50 \, cm$ is heated so that its radius increases at the rate of $1 \, mm$ per hour,then the rate at which the area of the plate increases (in $cm^2/hour$) is (in $\pi$)

If the error committed in measuring the radius of the circle is $0.05 \%$,then the corresponding error in calculating the area is (in $\%$)

$A$ ladder $5 \ m$ long rests against a vertical wall. If its top slides downwards at the rate of $10 \ cm/sec$,then the foot of the ladder is sliding at the rate of . . . . . . $m/sec$,when it is $4 \ m$ away from the wall.

The distance $s$ in meters covered by a particle in $t$ seconds is given by $s = 2 + 27t - t^3$. The particle will stop after covering a distance of: