Question

The volume Vr (in cubic meters) of a spherical balloon with radius r meters is given by =Vr43πr3. The radius Wt (in meters) after t seconds is given by =Wt+8t3. Write a formula for the volume Mt (in cubic meters) of the balloon after t seconds. It is not necessary to simplify.

Answer 1

Volume of balloon as a function of time is given by
`V(t)=(2048)/(3)\pi t^(9)m^(3)`

Explanation:

We know that volume of a sphere with radius 'r' is given by

`V_(r)=(4)/(3)\pi r^(3)`

Now it is given that radius as a function of time is given by

`r(t)=8t^(3)`

using this value in the relation for volume of the balloon we obtain volume as a function of time as

`V(t)=(4)/(3)\pi* (8t^(3))^(3)\\\\\therefore V(t)=(2048)/(3)\pi t^(9)m^(3)`