SOLUTION: Hi my question is : An orange is spherical. Suppose it grows so that its volume increases at an average rate of 4cm3 /day. a) Express the radius of the orange as a function o

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Question 1199151: Hi my question is :
An orange is spherical. Suppose it grows so that its volume increases at an average rate of
4cm3 /day.
a) Express the radius of the orange as a function of time t in days.
b) Determine the radius of the orange six weeks after it begins growing.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
An orange is spherical.
Suppose it grows so that it's volume increases at an average rate of 4cm3/day.
a) Express the radius of the orange as a function of time t in days.
Volume of a sphere: V = %284%2F3%29%2Api%2Ar%5E3
let t = no. of growing days
%284%2F3%29%2Api%2Ar%5E3 = 4t
Get rid of the denominator, multiply both sides by 3
4%2Api%2Ar%5E3 = 12t
r%5E3 = %2812t%29%2F%284%2Api%29
r%5E3 = %283t%29%2F%28pi%29
r = %28%283t%29%2F%28pi%29%29%5E%281%2F3%29
:
b) Determine the radius of the orange six weeks after it begins growing.
r = %28%284%2A6%29%2F%28pi%29%29%5E%281%2F3%29
r = %2818%2F%28pi%29%29%5E%281%2F3%29
r = 5.73%5E%281%2F3%29
r = 1.79 cm after 6 weeks