Question

the area of three adjacent faces of a cuboid are X Y and Z if its volume is V prove that V square is equal to x y z​

Answer 1

#BAL

let the dimensions of cuboid are

Length=l

breadth=b

height =h

given area of three faces x,y and z

lb= x--(1)

bh=y---(2)

lh= z---(3)

multiply (1),(2) and (3)

lb×bh×lh= xyz

l^2×b^2×h^2=xyz

(lbh)^2= xyz

v^2= xyz

since volume of the cuboid=v=lbh