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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.

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 rt for the radius in terms of t Find class=

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Solution

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

The final answer

Option D