SOLUTION: A spherical balloon is decreasing its volume at a rate of 163.87 cm3/min. Find the rate at which the radius is decreasing when the volume is 4916.12 cm3. Round to 5 significant

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Question 860002: A spherical balloon is decreasing its volume at a rate of 163.87 cm3/min. Find the rate at which the radius is decreasing when the volume is 4916.12 cm3.
Round to 5 significant digit
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
V=%284%2F3%29pi%2AR%5E3
Differentiate with respect to time.
dV%2Fdt=%284%2F3%29pi%2A%283R%5E2%29%28dR%2Fdt%29
163.87=4%2Api%2AR%5E2%2AdR%2Fdt
Now use the volume provided to find the radius at that instant.
%284%2F3%29pi%2AR%5E3=4916.12
R%5E3=1173.64
R=10.55
163.87=4%2Api%2A%2810.55%29%5E2%2A%28dR%2Fdt%29
dR%2Fdt=0.117 cm/min