A spherical iron ball 10cm in radius is coated with a layer of ice ofuniform thickness that melts at a rate of `50c m^3//m in`. When the thickness of ice is 5cm, then findthe rate at which the thickness of ice decreases.A. `(5)/(6pi)cm//min`B. `(1)/(54pi) cm//min`C. `(1)/(18pi) cm//min`D. `(1)/(36pi) cm//min`

A spherical iron ball 10cm in radius is coated with a layer of ice ofu

1.	A spherical iron ball 10cm in radius is coated with a layer of ice ofuniform thickness that melts at a rate of `50c m^3//m in`. When the thickness of ice is 5cm, then findthe rate at which the thickness of ice decreases.A. `(5)/(6pi)cm//min`B. `(1)/(54pi) cm//min`C. `(1)/(18pi) cm//min`D. `(1)/(36pi) cm//min`
Answer» Correct Answer - C Let at any time, h cm be the thickness of ice. Then, V=Volume of ice `=(4)/(3)pi(10+h)^(3)-(4)/(3)pixx10^(3)` `implies (dV)/(dt)=4pi(10+h)^(2)(dh)/(dt)` `implies -50=4pi (10+5)^(2)xx(dh)/(dt) " "[because (dv)/(dt)=-50 cm^(3)//min and h = 5]` `implies (dh)/(dt) = -(1)/(18pi) cm//min`

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