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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

`1cm//min`

B

`2cm//min`

C

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

D

`5cm//min`

Text Solution

Verified by Experts

The correct Answer is:
A
`"Given, "(dV)/(dt)=100pi cm^(3)//min`
`therefore" "(d)/(dt)((4)/(3)pir^(3))=100pi rArr 3r^(2)(dr)/(dt)=(300pi)/(4pi)" "rArr" "((dr)/(dt))_("(r = 5)")=(300)/(4xx3xx25)="1cmmin"`
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