SURFACE AREAS

AND VOLUMES

• CUBOID - Introduction

Examples :

Fish Aquarium

Brick

Boxes

Let us see few examples

of cuboid

l

b

Let us see geometrical

figure of cuboid

1

2

5

3

6

4

• A cuboid has six faces.

• Two horizontal faces.

1

2

3

1

4

2

• Four vertical faces.

• A cuboid has eight corners.

h

• A cuboid has three dimensions,

which are length (l ),

breadth (b) and height (h)

Vertical surface area

=

=

lh

+

lh

+

bh

+

bh

=

2lh

+

2bh

=

2

(l + b)

=

2

(l + b)h

h

Sum of areas of 4 vertical surfaces

Total surface area

+

+ 2

=

+ 2lb

2lh

(lb)

+ 2bh

Vertical surface

=

Area of 2 base faces

=

2

=

2 (l + b) h

= 2 (l + b) h

2 (lb + bh + lh)

Vertical Surface Area

Total Surface Area =

l

b

Let us see formulae

related to cuboid

Area of the shaded face

= b × h

h

Area of the shaded face

= l × h

Area of the shaded face

= l × h

A cuboid has 2 base faces

Area of the shaded face

= l × b

Let us first understand formula for vertical surface area of a cuboid

Let us now understand the formula for total surface area of cuboid

Area of rectangle = Product of adjacent sides

(lb + bh + lh)

Area of the shaded face

= b × h

l

b

h

l × b × h

Volume of cuboid =

Volume of cuboid is the

capacity of the cuboid

Let us consider the base

of the cuboid

What is the Area

of rectangular

base ?

l × b

Let us place another

rectangle of same

length and breadth

on it

What is the Area

two rectangles ?

2 × l × b

Let us place another

rectangle of same

length and breadth

on them

What is the Area of

3 rectangular bases ?

3 × l × b

Continuing the process

if we place ‘h’ such rectangles

on one another,

h × l × b

What is the space

occupied ?

h

What is the figure so

formed ?

Cuboid

3 × l × b

2 × l × b

l × b

∴ Volume of cuboid =

l × b × h

h × l × b