Water is being poured into a cylindrical vessel with a radius of $2 \text{ cm}$ at a rate of $8 \text{ cm}^3/\text{s}$. The rate at which the height of the water is increasing is:

If by dropping a stone in a quiet lake a wave moves in a circle at a speed of $3.5 \, cm/sec$,then the rate of increase of the enclosed circular region when the radius of the circular wave is $10 \, cm$ is ......... $cm^2/sec$. $\left( \pi = \frac{22}{7} \right)$

The radius of a circle is increasing at the rate of $2 \text{ cm/sec}$. The rate at which its area is increasing when the radius of the circle is $5 \text{ decimeters}$ 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.

$A$ kite is moving horizontally at a height of $151.5 \ m$. If the speed of the kite is $10 \ m/s$,how fast is the string being let out when the kite is $250 \ m$ away from the boy who is flying the kite? The height of the boy is $1.5 \ m$.

The radius of a circle is increasing at a rate of $0.7 \text{ cm/s}$. The rate at which the circumference of the circle is increasing is . . . . . . .