Suppose that the radius r and surface area `S=4pi r^(2)` of a sphere are differentiable functions of t. Write an equation that relates `(ds)/(dt)` to `(dr)/(dt)`.

The rate of change of surface area of a sphere w.r.t. radius is ………..

Rate of increase in surface area of a sphere w.r.t radius is ……….

Let f:[0,4]rarr R be a differentiable function then for some alpha,beta in (0,2)int_(0)^(4)f(t)dt

solve the differential equation (1+t^2)dx/dt=2t

Given that s=t^(2)+2t+3 . Find (ds)/(dt) .

Twenty seven solid iron spheres,each of radius r and surface area S are melted to form a sphere with surface area S'. Find the radius r of the new sphere.ratio of S and S.

Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S ' . Find the radius r of the new sphere. ratio of S and S .

Twenty-seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S'. Find the (i) radius r' of the new sphere, (ii) ratio of S and S'.