If the error committed in measuring the radius of the circle is $0.05 \%$,then the corresponding error in calculating the area is (in $\%$)

$A$ kite is moving horizontally at a height of $151.5 \ m$. If the speed of the kite is $10 \ m/s$,how fast is the string being let out when the kite is $250 \ m$ away from the boy who is flying the kite? The height of the boy is $1.5 \ m$.

The side of a square piece is increasing at a rate of $4 \text{ cm/min}$. Find the rate at which the area is increasing when the side is $8 \text{ cm}$ long.

$A$ man $2 \text{ m}$ tall walks at the rate of $1 \frac{2}{3} \text{ m/s}$ towards a street light which is $5 \frac{1}{3} \text{ m}$ above the ground. The rate at which the length of his shadow is changing when he is $3 \frac{1}{3} \text{ m}$ away from the base of the light is . . . . . . (in $\text{ m/s}$)

$A$ spherical iron ball of radius $10 \ cm$ is coated with a layer of ice of uniform thickness. The ice melts at a rate of $50 \ cm^3/min$. When the thickness of the ice is $5 \ cm$,the rate at which the thickness of the ice decreases is:

$A$ stone is dropped into a quiet lake and waves move in circles at the speed of $ 5 \text{ cm s}^{-1} $. At that instant,when the radius of the circular wave is $ 8 \text{ cm} $,how fast is the enclosed area increasing?