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

Answer:

Volume of balloon as a function of time is given by $V(t)=\frac{2048}{3}\pi t^{9}m^{3}$

Step-by-step explanation:

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

$V_{r}=\frac{4}{3}\pi r^{3}$

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

$V(t)=\frac{4}{3}\pi\times (8t^{3})^{3}\\\\\therefore V(t)=\frac{2048}{3}\pi t^{9}m^{3}$