If $r$ is the radius of a spherical balloon at time $t$ and the surface area of the balloon changes at a constant rate $K,$ then ....

Consider an expanding sphere of instantaneous radius $R$ whose total mass remains constant. The expansion is such that the instantaneous density $\rho$ remains uniform throughout the volume. The rate of fractional change in density $\left(\frac{1}{\rho} \frac{d \rho}{dt}\right)$ is constant. The velocity $v$ of any point on the surface of the expanding sphere is proportional to

If $pv = 81$,then $\frac{dp}{dv}$ at $v = 9$ is equal to

The radius of a sphere increases at the rate of $0.04 \text{ cm/sec}$. The rate of increase in the volume of that sphere with respect to its surface area,when its radius is $10 \text{ cm}$ is

An edge of a variable cube is increasing at the rate of $3 \, cm/s$. How fast is the volume of the cube increasing when the edge is $10 \, cm$ long?

The two equal sides of an isosceles triangle with a fixed base $b$ are decreasing at the rate of $3 \ cm/s$. How fast is the area decreasing when the two equal sides are equal to the base?