The radius of a circle is increasing at the rate of $2 \text{ cm/sec}$. The rate at which its area is increasing when the radius of the circle is $5 \text{ decimeters}$ is:

The radius of a right circular cylinder increases at a constant rate. Its altitude is a linear function of the radius and increases three times as fast as the radius. When the radius is $1 \, cm$,the altitude is $6 \, cm$. When the radius is $6 \, cm$,the volume is increasing at the rate of $1 \, cm^3/sec$. When the radius is $36 \, cm$,the volume is increasing at a rate of $n \, cm^3/sec$. The value of $n$ is equal to:

If a balloon lying at an altitude of $30 \ m$ from an observer at a particular instant is moving horizontally at the rate of $1 \ m/s$ away from him, then the rate at which the balloon is moving away directly from the observer at the $40^{\text{th}}$ second is (in $m/s$)

$A$ particle moves along the curve $y = x^2 + 2x$. At what point on the curve do the $x$ and $y$ coordinates of the particle change at the same rate?

$A$ spherical snowball is melting such that its volume is decreasing at the rate of $8 \text{ cm}^3/\text{s}$. Find the rate of change of the radius when the radius is $2 \text{ cm}$.

The volume of a sphere increases at the rate of $\pi \text{ cm}^3/\text{s}$. When the radius is $2 \text{ cm}$,the rate at which the radius increases is . . . . . . $\text{cm/s}$.