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Sand falls on to horizontal ground at the rate of $$9m^3$$ per minute and forms a heap in the shape of a right circular cone with vertical angle $$60^{\circ}$$. Show that 10 seconds after the sand begins to fall, the rate at which the radius of the base of the pile is increasing is $$3^{\frac{1}{2}}(\frac{4}{\pi})^{\frac{1}{3}}m$$ per minute.