Question

A balloon (in the shape of a sphere) is being inflated. The radius is increasing at a rate of 5 cm per second. Find a function, r(t), for the radius in terms of t. Find a function, V(r), for the volume of the balloon in terms of r. Find (V ∘ r)(t). Hint: the volume of a sphrere is 4/5πr3.

Answer 1

`\begin{gathered} r^1(t)=5 \\ r(t0=5t \end{gathered}`
`\begin{gathered} V=(4)/(3)\pi r^3 \\ \\ (V.r)t=(4)/(3)\pi(5t)^3 \\ \\ =(500\pi t^3)/(3) \end{gathered}`

The final answer

Option D