The document discusses the volume and surface area of different shapes. It defines volume as the space occupied by an object and surface area as the area of a face. It provides the formulas for calculating the volume of a cylinder as πr^2h, a cone as 1/3πr^2h, and a sphere as 4/3πr^3. Examples are given of applying the formulas to find the volume of each shape using given radius and height values.

1. Volume And Surface Area
Class:VIII

2. What similarities do you see in the
pictures below ?

3. 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

4. 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

5. VOLUME OF CYLINDER = AREA OF BASE x HEIGHT
HEIGHT= h
AREA OF BASE =
AREA OF A CIRCLE
= лr2
VOLUME OF THE CYLINDER = лr2 h
If the value of л is not given , take л = 22/7 .

6. -------------------
 ARYABHATTA GAVE THE VALUE OF Π

7. 7 cm
15 cm

9. 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
O
P
The angle between the height of the cone and a radius of the
base is a right angle .

10. 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

11. 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

13. SPHERE
VOLUME OF A SPHERE
Volume of a sphere = 4/3 л r 3
r

14. 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

15. SHAPES VOLUME
CYLINDER
π r2h
CONE
1/3 π r2 h
SPHERE
4/3 π r3
SUMMARy

16. 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 ?