If r is the radius, S the surface area and V the volume of a spherical bubble, prove that
(i) `(dV)/(dt)=4pir^(2)(dr)/(dt)`

If r is the radius, S the surface area and V the volume of a spherical bubble, prove that (ii) (dV)/(dS) prop r

If S denotes the surface area of a sphere and V volume, Prove that S^(3)=36piV^(2) .

If h,C,V represent height, curved surface area, and volume of cone, prove that 3piVh^(3)-C^(2)h^(2)+9V^(2)=0 .

Twenty seven solid iron spheres, each of radius r and surface area S aer melted to form a sphere with surface area S^(1). Find the (i) radius r_(1) of the nw sphere (ii) ratio of S and S^(1)

If V denotes the volume of a cube and 'S' its surface area, then prove that S^3=216V^2 .

The rate of change of the volume of the sphere w.r.t its surface area, when its radius is 2cm is

Twenty seven solid iron sphere, 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.

A toy is in the form of a hemisphere surmounted by a right circular cone of same base radius. If the radius of the base of the cone is 21 cm and its volume is 2/3 volume of hemisphere, calculate the height of the cone and the total curved surface area of the toy.

Find the order and degree of the differential equation, ((ds)/(dt))^4+3s(d^2s)/(dt^2)=0