Ive never seen this type of problem before but i got it for homework today.
A spherical ballon is being inflated in such a way that its radius is increasing at the constant rate of 3cm/min. If the volume of the balloon is 0 at time 0, at what rate is the Volume increasing after 5 minutes?
I think the equation is sorta like V(r) = 4r3/3 but that is for feet and I need cm.
A spherical ballon is being inflated in such a way that its radius is increasing at the constant rate of 3cm/min.⇒drdt=3cm/min
The relation between the volume and radius of the spherical ballon is v(r)=4∗r3/3
The dervative of volume v respect to variable v is dvdr=4r2
At time 5 minutes dvdr=4∗52=100cm^2
Applying chain rule,dvdt=dvdr∗drdt
dvdt=100∗cm2∗3cm/min=300cm3/min
This is a kind of problem relative rate of change,application of differvative.