The rate of change of the area of a circle with respect to its radius $r$ at $r = 6 \text{ cm}$ is

The radius of a cylinder is increasing at the rate of $2 \text{ cm/sec}$ and its height is decreasing at the rate of $3 \text{ cm/sec}$. Find the rate of change of volume when the radius is $3 \text{ cm}$ and the height is $5 \text{ cm}$.

Each edge of a cube is expanding at the rate of $1 \text{ cm/sec}$. Then the rate (in $\text{cc/sec}$) of change in its volume,when each of its edge is of length $5 \text{ cm}$,is

$A$ man of $5 \text{ feet}$ height is walking away from a light fixed at a height of $15 \text{ feet}$ at the rate of $K \text{ miles/hour}$. If the rate of increase of his shadow is $\frac{11}{5} \text{ feet/sec}$,then $K=$ (Take $1 \text{ mile} = 5280 \text{ feet}$)

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

$A$ particle moves in a straight line so that its velocity at any point is given by ${v^2} = a + bx$,where $a, b \neq 0$ are constants. The acceleration is