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Question: Answered & Verified by Expert
A spherical iron ball of 10cm radius is coated with a layer of ice of uniform thickness that melts at a rate of 50cm3/min . When the thickness of ice is 5cm , then the rate (in cm/min .) at which of the thickness of ice decreases, is:
MathematicsApplication of DerivativesJEE MainJEE Main 2020 (09 Jan Shift 1)
Options:
  • A 56π
  • B 154π
  • C 136π
  • D 118π
Solution:
2145 Upvotes Verified Answer
The correct answer is: 118π
Let thickness =x cm
Total volume V=43π10+x3
dVdt=4π10+x2dxdt..(i)
Given dVdt=50 cm3/min
At x=5 cm
50=4π10+52dxdt
dxdt=118π cm/min

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