The rate of change of the area of a circle with respect to its radius at $r = 3 \text{ cm}$ is . . . . . . $\text{cm}^2/\text{cm}$. (in $\pi$)

The surface area of a spherical balloon is increasing at the rate of $2 \text{ cm}^2/\text{sec}$. Find the rate of increase in the volume of the balloon when the radius of the balloon is $6 \text{ cm}$.

The volume $V$ and depth $x$ of water in a vessel are connected by the relation $V = 5x - \frac{x^2}{6}$. If the volume of water is increasing at the rate of $5 \, cm^3/sec$,find the rate at which the depth of water is increasing when $x = 2 \, cm$.

If $f(x) = x^{2}$,find $\frac{f(1.1) - f(1)}{1.1 - 1}$.

$A$ particle moves along the curve $y=x^2+2x$. Then, the point on the curve such that the $x$ and $y$ coordinates of the particle change with the same rate is

The point on the curve $y^2 = 18x$,at which the rate of change of $Y$-coordinate is twice the rate of change of $X$-coordinate is . . . . . . . $\left(\frac{dx}{dt} \neq 0\right)$