The radius of a circular plate is increasing at the rate of $0.01 \text{ cm/sec}$. When the radius is $12 \text{ cm}$, the rate at which the area increases is (in $\text{cm}^2/\text{sec}$): (in $\pi$)

The radius of a sphere increases at the rate of $0.04 \text{ cm/sec}$. The rate of increase in the volume of that sphere with respect to its surface area,when its radius is $10 \text{ cm}$ is

An object is moving in the clockwise direction around the unit circle $x^2+y^2=1$. As it passes through the point $\left(\frac{1}{2}, \frac{\sqrt{3}}{2}\right)$,its $y$-coordinate is decreasing at the rate of $3 \text{ units/sec}$. The rate at which the $x$-coordinate changes at this point is

$A$ ladder of length $10 \ m$ is resting against a vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $2 \ m/min$. How fast is its height on the wall decreasing when the foot of the ladder is $6 \ m$ away from the wall?

The volume of a spherical ball is increasing at a rate of $4 \pi \text{ cm}^3 \text{ s}^{-1}$. The rate at which its radius increases,when its volume is $288 \pi \text{ cm}^3$,is ....... $\text{cm s}^{-1}$.

$A$ square plate is contracting at the uniform rate $4 \,cm^2 / sec$. The rate at which the perimeter is decreasing, when the side of the square is $20 \,cm$, is