Sphere: radius rate from volume rate

3 Air is being pumped into a balloon in the shape of a sphere so that its volume is increasing at a constant rate of \(50 \mathrm {~cm} ^ { 3 } \mathrm {~s} ^ { - 1 }\). Find the rate at which the radius of the balloon is increasing when the radius is 10 cm .

4 The volume of a sphere, \(V \mathrm {~cm} ^ { 3 }\) is given by the formula \(V = \frac { 4 } { 3 } \pi r ^ { 3 }\) where \(r \mathrm {~cm}\) is the radius.
The radius of a sphere increases at a constant rate of 2 cm per second.
Find the rate of increase of \(V\) when \(r = 10 \mathrm {~cm}\).

A spherical balloon of radius \(r\) cm has volume \(V\) cm\(^3\), where \(V = \frac{4}{3}\pi r^3\). The balloon is inflated at a constant rate of 10 cm\(^3\) s\(^{-1}\). Find the rate of increase of \(r\) when \(r = 8\). [5]

The volume of a spherical bubble is increasing at a constant rate. Show that the rate of increase of the radius, \(r\), of the bubble is inversely proportional to \(r^2\) Volume of a sphere = \(\frac{4}{3}\pi r^3\) [4 marks]

Air is pumped into a spherical balloon at the rate of 250 cm\(^3\) per second. When the radius of the balloon is 15 cm, calculate the rate at which the radius is increasing, giving your answer to three decimal places [3]