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 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 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)

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 ratio of S and S'.

The area of three adjacent faces of a cube are x,y and z. if its volume is V, prove that V=sqrt(xyz) .

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.

The radius of a sphere is 21 cm. calculate its surface area and volume.