The volume of a spherical balloon is increasing at the rate of $40 \ cm^3/\min$. The rate of change of the surface area of the balloon at the instant when its radius is $8 \ cm$ is ........ $cm^2/\min$.

If the radius $r$ of a sphere is increasing at a rate of $2 \text{ cm/s}$,then the rate of change of its surface area is proportional to which of the following?

The displacement $x$ of a particle at time $t$ is given by $x = At^2 + Bt + C$,where $A, B, C$ are constants and $v$ is the velocity of the particle. Then the value of $4Ax - v^2$ is:

If the surface area of a cube is increasing at a rate of $3.6 \text{ cm}^2/\text{sec}$,while maintaining its shape,then the rate of change of its volume (in $\text{cm}^3/\text{sec}$),when the length of a side of the cube is $10 \text{ cm}$,is:

$A$ rod of length $41 \ ft$ with an end $A$ on the floor and another end $B$ on the wall perpendicular to the floor is sliding away horizontally from the wall at the rate of $3 \ ft/min$. When the end $B$ is at a height of $9 \ ft$ from the floor,the rate at which the area of the triangle formed by the rod with the wall and the floor changes at that instant is (in $ft^2/min$):

The equation of motion of a car is $s = t^2 - 2t$,where $t$ is measured in hours and $s$ in kilometers. When the distance travelled by the car is $15 \, km$,the velocity of the car is ......... $km/h$.