Question

If the areas of the three adjacent faces of a cuboidal box are 120sq.Cm, 72sq.Cm and 60sq.Cm respectively, find the volume of the box.

Answer 1

720sq cm
vol= lbh
l*b=120
b*h=72
h*l=60
lbh=√(120*72*60) = 720

Answer 2

ANSWER :-

GIVEN:-

• Length = l
• Breadth = b
• Height = h
• Area of three adjacent faces of the cuboid are : 120 cm^2 ; 72 cm^2 ; 60 cm^2.

ATQ,

l × b = 120 ...............(1)

l × h = 72 ...................(2)

b × h = 60  ................(3)

Multiplying (1), (2) and (3), we get

(l × b) × (l × h)  × (b × h) = 518400.............(4)

And,

Volume of the cuboid = l × b × h

∴ V = l b h

Squaring on both sides, we get

 

V^2 = l^2 × b^2 × h^2

 

∴ V^2 = 518400.

Taking square root on both the sides,

we get,

 V = 720 cm^3.

WHAT IS A CUBOID?

◇ A cuboid is a three dimensional figure

◇ It has 6 faces and 8 vertices.

◇ It has 12 edges.

◇ Example : Box, book, etc...

◇ It forms a convex polyhedron.

◇ It has a solid composition.

◇ A cuboid is also known as a rectangular prism.

◇ All cubes are cuboids.

◇ All cuboids are not cubes.