Calculus 1 homework question

Question

It is your friend's birthday tomorrow, and you are planning a surprise party for them. For this party, you got perfectly spherical balloons and you are filling these balloons with helium. The helium enters that balloon at a rate of 100 cm3/s (i.e. the volume of the balloon is increasing at this rate). How quickly is the radius of the balloon changing when the diameter of the balloon is 35 cm? Do not include units in your answer.

Answer 1

Relation between Volume and radius: V = (4/3)πr³

Now relate rates by taking the derivative with respect to time of both sides:

dV/dt = 3(4/3)πr²(dr/dt) = 4πr²(dr/dt)

Rearrange.

dr/dt = (dV/dt)/(4πr²)

dV/dt = 100 cm³/s and r = 35/2 = 17.5cm

dr/dt == 100 / 4*pi*(17.5)²

dr/dt = 100/1225pi = 1/12.25pi cm/s