The radius 𝑟 , in inches, of a spherical balloon is related to the volume 𝑉 by r(V)=3√3V/4π.Air is pumped into the balloon so the volume after 𝑡 seconds is given by 𝑉(𝑡)=10+18𝑡.

Question

Find an expression for the composite function 𝑟(𝑉(𝑡))

What is the exact time in seconds when the radius reaches 16 inches?

Answer 1

r(V)=3√3V/4π

𝑉(𝑡)=10+18𝑡

We want r(t). Use the second equation for V(t) in the first:

r(t)=3√3(10+18𝑡)/4π

r(t) = 4.1350 + 7.4429t [The radius as a function of time]

16 = 4.1350 + 7.4429t

t = 1.59 seconds