If the radius of a spherical balloon is increasing at the rate of $5 \text{ inch/min}$, then the rate at which the volume increases (in $\text{cubic inches/min}$) when the radius is $10 \text{ inches}$ is: (in $\pi$)

The law of motion of a body moving along a straight line is $x = \frac{1}{2} vt$,where $x$ is its distance from a fixed point on the line at time $t$ and $v$ is its velocity. Then:

The sides of an equilateral triangle are increasing at the rate of $2 \, cm/sec$. The rate at which the area increases,when the side is $10 \, cm$ is:

The diagonal of a square is changing at the rate of $0.5 \text{ cm/sec}$. Then the rate of change of area when the area is $400 \text{ cm}^2$ is equal to

The $x$-coordinate changes on the curve $y=3x^5+15x-8$ at the rate of $\frac{1}{5} \text{ units/sec}$. If $A(x_1, y_1)$ and $B(x_2, y_2)$ are the points on the curve at which the $y$-coordinate changes at the rate of $6 \text{ units/sec}$,then the slope of $AB$ is:

The radius of a right circular cylinder increases at the rate of $0.1 \text{ cm/min}$,and the height decreases at the rate of $0.2 \text{ cm/min}$. The rate of change of the volume of the cylinder,in $\text{cm}^3/\text{min}$,when the radius is $2 \text{ cm}$ and the height is $3 \text{ cm}$ is