The areas of three adjacent faces of a cuboid are x, y and z. If the volume is V, prove that `V^2 = xyz`.

The areas of three adjacent faces of a cuboid are x ,\ y\ a n d\ zdot If the volume is V , prove that V^2=x y zdot

If the areas of three adjacent faces of a cuboid are 8\ c m^2,\ 18 c m^2a n d\ 25 c m^2dot Find the volume of the cuboid.

If A_1,\ A_2a n d\ A_3 denote the areas of three adjacent faces of a cuboid, then its volume is (a) A_1A_2\ A_3 (b) 2A_1A_2A_3 (c) sqrt(A_1\ A_2A_3) (d) A_1A_2A_3

In the adjacent figure, find x+y+z

The sum of the surface areas of a cuboid with sides x ,2x and x/3 and a sphere is given to be constant. Prove that the sum of their volumes is minimum, if x is equal to three times the radius of sphere. Also find the minimum value of the sum of their volumes.

Show that the product of the areas of the floor and two adjacent walls of a cuboid is the square of its volume.

If in Delta ABC , the distance of the vertices from the orthocenter are x,y, and z then prove that (a)/(x) + (b)/(y) + (c)/(z) = (abc)/(xyz)

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

Statement 1: Let veca, vecb, vecc be three coterminous edges of a parallelopiped of volume V . Let V_(1) be the volume of the parallelopiped whose three coterminous edges are the diagonals of three adjacent faces of the given parallelopiped. Then V_(1)=2V . Statement 2: For any three vectors, vecp, vecq, vecr [(vecp+vecq, vecq+vecr,vecr+vecp)]=2[(vecp,vecq,vecr)]

If V is the volume of a cuboid of dimensions a , b , ca n dS is its surface area, then prove that S/V = 2(1/a+1/b+1/c)