If a circular iron sheet of radius $30 \, cm$ is heated such that its area increases at the uniform rate of $6\pi \, cm^2/hr$,then the rate (in $cm/hr$) at which the radius of the circular sheet increases is

The radius of a circle is increasing at a rate of $0.1 \text{ cm s}^{-1}$. Then the rate of change of area,when its radius is $5 \text{ cm}$,is .........

$A$ sphere increases its volume at the rate of $\pi \text{ cm}^3/\text{s}$. The rate at which its surface area increases when the radius is $1 \text{ cm}$ 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 $1 \text{ mile} = 5280 \text{ feet}$)

Let $B \equiv (0,3)$ and $C \equiv (4,0)$. The point $A$ is moving on the line $y=2x$ at the rate of $2 \text{ units/second}$. The area of $\triangle ABC$ is increasing at the rate of

The edge of a cube is decreasing at the rate of $0.04 \ cm/sec$. If the edge of the cube is $10 \ cm$,then the rate of decrease of the surface area of the cube is...