The rate of change of the area of a sphere with respect to its radius, when the radius is $6 \text{ cm}$, is . . . . . . . (in $\pi$)

By dropping a stone in a quiet lake,a wave in the form of a circle is generated. The radius of the circular wave increases at the rate of $2.1 \text{ cm/sec}$. Then the rate of increase of the enclosed circular region,when the radius of the circular wave is $10 \text{ cm}$,is (Given $\pi = \frac{22}{7}$)

The radius of a circular plate is increasing at the rate of $0.01 \text{ cm/s}$ when the radius is $12 \text{ cm}$. Then,the rate at which the area increases,is

The radius of a circle is increasing at the rate of $0.7 \, cm/s$. What is the rate of increase of its circumference?

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

The radius of a cylinder is increasing at the rate of $5 \ cm/min$,so that its volume remains constant. When its radius is $5 \ cm$ and height is $3 \ cm$,the rate of decrease of its height is .......... $cm/min$.