A spherical balloon is inflated with a gas at a rate of 240 cubic centimeters per minute. How fast is the radius of the balloon increasing at the instant the radius is 30 cm?

Question

jtvatsim · Answer

Welcome to OpenStudy! Is this a question from Calculus class?

anonymous · Answer

yes it is.

freckles · Answer

so we have a sphere 
do you know the formula for a sphere ?

freckles · Answer

well the volume of a sphere that is

anonymous · Answer

Volume- (4/3) (pi)(r)^3

freckles · Answer

ok differentiate that equation w.r.t r

freckles · Answer

$$V(r)=\frac{4}{3}\pi r^3 $$
that is find:
$$\frac{dV}{dr}$$

freckles · Answer

do you know how to find:
$$\frac{d(r^3)}{dr}=?$$

anonymous · Answer

not really

freckles · Answer

have you guys talked about power rule ?

anonymous · Answer

no. my teacher does not explain anything right

freckles · Answer

have you guys talked about definition of derivative?

freckles · Answer

could you evaluate this limit:
$$\frac{d(r^3)}{dr}=\lim_{h \rightarrow 0}  \frac{(r+h)^3-r^3}{h}$$

freckles · Answer

try expanding (r+h)^3 first