Volume And Surface Area

Class:VIII

What similarities do you see in the

pictures below ?

The measure of the place occupied

by an object in space is called its

Volume

&.

The area of a face is called the Surface Area

CYLINDER :

A cylinder has THREE surfaces . TWO surfaces are

flat and circular . The remaining surface is curved ,

This is called the Curved Surface of the cylinder .

Curved surface

Base

VOLUME OF CYLINDER = AREA OF BASE x HEIGHT

AREA OF BASE =

HEIGHT= h

VOLUME OF THE CYLINDER = лr2 h

If the value of л is not given , take л = 22/7 .

AREA OF A CIRCLE

= лr2

-------------------

ARYABHATTA GAVE THE VALUE OF ∏

7 cm

15 cm

A cone has one circular flat surface and one curved surface .

Seg PA (h) is the height of the cone

Seg 0P (r) is the radius of the base .

Seg AO (l) is the slant height of the

cone .

A

OP

The angle between the height of the cone and a radius of the base is a right angle .

VOLUME OF A CONE = 1/3 ×AREA OF BASE ×HEIGHT

Height = h

Area of a base = Area of a circle

Area of a circle = r2

Volume of a cone = 1/3 r2 h

r

r = 3 cm , h = 14 cm

Volume of a cone = 1/3 л ґ2 h

= 1/3 x 22/7 x 3 cm x 3 cm x 14 cm

= 22 x 1 cm x 3 cm x 2 cm

= 132 cm3

0R

= 132 cu cm

SPHERE

VOLUME OF A SPHERE

Volume of a sphere = 4/3 л r 3r

GIVEN : r = 2.1 cm

Volume of a sphere = 4/3 л ґ3

= 4/3 x 22/7 x 2.1 cm x 2.1 cm x 2.1 cm

= 38.808 ( cm x cm x cm )

= 38.808 cm3

or

38.8o8cu cm

r

SHAPES VOLUME

CYLINDER

π r2h

CONE

1/3 π r2 h

SPHERE

4/3 π r3

SUMMARy

EVALUATION

How many surface does a cylinder has ?

What is the formula of a volume of a cone ?

What is the angle between the height and the base of a cone ?