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A spherical iron ball 10cm in radius is ...

A spherical iron ball 10cm in radius is coated with a layer of ice of uniform thickness that melts at a rate of `50c m^3//m in` . When the thickness of ice is 5cm, then find the rate at which the thickness of ice decreases.

A

`(1)/(54pi)` cm/min

B

`(5)/(6pi)` cm/min

C

`(1)/(36pi)` cm/min

D

`(1)/(18pi)` cm/min

Text Solution

Verified by Experts

The correct Answer is:
D
`V=(4)/(3)pi(x+10)^(3)` where x is thickness of ice.
`(dV)/(dt)=4pi(10+x)^(2)(dx)/(dt)`
At `x=5,((dx)/(dt))=(1)/(18pi)(cm)/(min)`
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