The radius of a circle is increasing uniformly at the rate of $3 \, cm/s$. The rate of increase of its area when the radius is $10 \, cm$ will be:

The volume of a cube is increasing at the rate of $8 \, cm^{3}/s$. How fast is the surface area increasing when the length of an edge is $12 \, cm$?

The diameter of one of the bases of a truncated cone is $100 \, mm$. If the diameter of this base is increased by $21 \%$ such that it still remains a truncated cone with the height and the other base unchanged,the volume also increases by $21 \%$. The radius of the other base (in $mm$) is

The point on the curve $6y = x^3 + 2$ at which the $y$-coordinate is changing $8$ times as fast as the $x$-coordinate is:

$A$ ladder $5 \ m$ in length is resting against a vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $1.5 \ m/sec$. The rate at which the height of the top of the ladder decreases when the foot of the ladder is $4.0 \ m$ away from the wall is .......... $m/sec$.

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