If the surface area of a spherical balloon of radius $6 \text{ cm}$ is increasing at the rate $2 \text{ cm}^2/\text{sec}$,then the rate of increase in its volume in $\text{cm}^3/\text{sec}$ is

$A$ particle moves along the curve $6y = x^3 + 2$. Find the points on the curve at which the $y$-coordinate is changing $8$ times as fast as the $x$-coordinate.

$A$ circular disc of radius $3 \text{ cm}$ is being heated. Due to expansion,its radius increases at the rate of $0.05 \text{ cm/s}$. Find the rate at which its area is increasing when the radius is $3.2 \text{ cm}$.

$A$ 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:

$A$ point is moving on $y=4-2x^2$. The $x$-coordinate of the point is decreasing at the rate of $5 \text{ units/s}$. Then, the rate at which the $y$-coordinate of the point is changing when the point is at $(1, 2)$ is

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