Introduction

In our every-day life , we come across objects like a wooden box, a match box, tea -packet, a chalk box, a book etc. All these objects are of similar shape. In fact, All these objects are made of six rectangular plane regions. These objects are in the shape of a cuboid.

Cuboid

 

A cuboid has six faces, 12 edges and 8 vertices

Any face of a cuboid may be called as the base of the cuboid. In that case, the four faces which meet the base are called the lateral faces of the cuboid.

 

Volume of a cuboid

Area of the base X Height

i.e. Length X Breadth X Height

If l is the length of the cuboid, b is its breadth,h is its height

then volume =lbh

So if you had a cuboid measuring 3cm by 4cm by 8cm,

 

V = lbh
V = 3 cm × 4 cm × 8 cm
V = 96 cm³

Surface Area

Calculating the surface area of a cuboid is very simple. Since there are six faces you can calculate the area of each face and then add them together:

Surface Area (S.A.) = lb + lb + lh + lh + hb + hb
S.A. = 2lb + 2lh + 2hb

So if you had a cuboid measuring 3cm by 4cm by 8cm, you would calculate the surface area thus:

S = 2 × (3×4) + 2 × (4×8) + 2 × (3×8)
S = 2×12 + 2×32 + 2×24
S = 24 + 64 + 48
S = 136cm²

Lateral surface Area

The sum of areas of four faces leaving the bottom and top faces is called lateral surface area

If l is the length of the cuboid, b is its breadth,h is its height

Lateral surface area (L.S.A.) = 2(l + b) h

e.g. The lateral surface area of a cuboid with dimensions length 8cm,height 4cmand breadth 3cm is

2(3+8)x4 =48 cm²

Diagonal of a cuboid

The length of diagonal of a cuboid is √(l²+b²+h²)

Remark While finding the volume ,surface area r lateral surface area of a cuboid, its length,breadth and height must be expressed in the same units