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A spherical iron ball of radius 10cm, co...

A spherical iron ball of radius 10cm, coated with a layer of ice of uniform thickness, melts at a rate of `100 pi cm^(3) //` min.The rate at which the thickness decreases when the thickness of ice is 5 cm, is

A

`1 cm// ` min

B

`2 cm //`min

C

`(1)/( 376) cm //` min

D

`5 cm //` min

Text Solution

Verified by Experts

Given, `(dV)/(dt) =100 pi cm^(3) //`min
`(d)/(dt) ((4)/(3) pir^(3))=100pi rArr 3r^(2) (dr)/( dt)=(300pi)/(4pi) rArr((dr)/(dt))_((r= 5)) = ( 300)/( 4 xx 3 xx 25) = 1 cm//` min
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