Question
The radius r, in inches, of a spherical balloon is related to the volume V by r(V)= cubed√3V/4pi
Air is pumped into the balloon so the volume after t seconds is given by V(t)=12+20t.
a. Find the expression for the composite function r(V(t)).
b. What is the exact time in seconds when the radius reaches 16 inches?
Air is pumped into the balloon so the volume after t seconds is given by V(t)=12+20t.
a. Find the expression for the composite function r(V(t)).
b. What is the exact time in seconds when the radius reaches 16 inches?
Answers
oobleck
r = ∛(3V/(4π)) = ∛(3(12+20t)/(4π)) = ∛(3(3+5t)/π)
∛(3(3+5t)/π) = 16
3(3+5t)/π = 4096
3+5t = 4096π/3
t = (4096π - 9)/15
∛(3(3+5t)/π) = 16
3(3+5t)/π = 4096
3+5t = 4096π/3
t = (4096π - 9)/15