If $$y=\sin (\sin x)$$ and $$y^{\prime \prime}+f(x) \cdot y^{\prime}+g(x) \cdot y=0$$, then $$f(x) \cdot g(x)$$ is equal to

A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness, which melts at a rate of 50 cm$$^3$$ /min. When the thickness of the ice is 15 cm, the rate at which the thickness of ice decreases is ........ cm/min.

Find the minimum value of $$2x+3y$$, when $$xy=6$$.

The volume of a spherical balloon is increasing at the rate of $$30 \mathrm{~cm}^3$$ per minute. Find the rate of change of surface area of the balloon, when its radius is $$6 \mathrm{~cm}$$.