The radius of a circle is increasing at a rate of $0.7 \text{ cm/s}$. The rate at which the circumference of the circle is increasing is . . . . . . .

$A$ balloon starting from rest is ascending from the ground with a uniform acceleration of $4 \ ft/sec^2$. At the end of $5 \ sec$, a stone is dropped from it. If $T$ is the time taken for the stone to reach the ground and $H$ is the height of the balloon when the stone reaches the ground, then:

On dropping a stone in stationary water,circular ripples are observed. The rate of flow of ripples is $6 \text{ cm/sec}$. When the radius of the circle is $10 \text{ cm}$,the rate of increase in its area is:

Let $S$ be the focus of $y^2 = 4x$ and a point $P$ is moving on the curve such that its abscissa is increasing at the rate of $4 \text{ units/sec}$. Then the rate of increase of the projection of $SP$ on the line $x + y = 1$ when $P$ is at $(4, 4)$ is:

The volume of a cube is increasing at a rate of $9 \text{ cm}^3/\text{s}$. How fast is the surface area increasing when the length of an edge is $10 \text{ cm}$ (in $\text{ cm}^2/\text{s}$)?

Let a kind of bacteria grow following the function $f(t) = t^4$,where $t$ is given in seconds. If the rate of growth of the bacteria after $t_0$ seconds is $4000 \text{ units/second}$,then $t_0 =$