2. SUBJECT: MATHS
PRESENTED BY : MONA A. PATIL
ROLL NO.: 68
YEAR: 2011-2012

3. CONTENTS
CONE
VOLUME OF CONE

4. INTRODUCTION
 In previous class we have studied about volume and
surface area of a cylinder.

6.  What do we called this shape?
a) Triangle
b) Cone
c) Cylinder

7. Today we are going to study
about the volume of a Cone.

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

9.  In the diagram alongside,
seg OA (h) is the height of the cone.
seg AP (r) is the radius of the cone.
seg OP (l) is the slant height of the cone.

10. In diagram alongside ∠A = 90̊
A
O
P

11. B
A
C

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

14. The measure of the space occupied by any cone is
called volume of the Cone.

15. Volume of a Cone =1/3 x area of base x height
.

16. Base of a Cone is a circle.
What is the area of a circle?
a) πr2
b) 2πr
c) πd

17.  Area of base = πr2
∴ volume of a cone = 1/3 xπr2x h
= 1/3 πr2h

18. 1. The height of a cone is 14cm and the radius of its base is
3cm. What is its volume?
Solution : Here, r= 3cm, h= 14cm
Volume of cone = 1/3πr2h
= 1/3x 22/7 x 3x3 x14
= 22x 3 x9
= 132 cu.cm

19. 2. Find the volume of a cone of height 7cm and a base radius
of 9cm.
Solution: Here, r = 9cm , h = 7cm
Volume of Cone = 1/3πr2h
= 1/3 x 22/7 x 9 x 9 x 7
= 22 x 3 x9
= 594 cu. cm

20. 3.The radius of the base of a cone is 5cm and it’s slant
height is 13cm. Find the volume of the
cone.(π=3.14)
Solution: here r=5cm, l=13cm
To find out the volume of the cone we require height(h)
of the cone.

21. The height and the radius of a cone form a right
angle.
So we will use ‘Pythagoras’ theorem to find out he
height of the cone.

22. Using Pythagoras theorem
l2 = r2 + h2
∴ 132 = 52 + h2
∴ h2 = 132 – 52
∴ h2 = 169– 25
∴ h2 = 144
∴ h = 12

23. Volume of a cone = 1/3πr2h
= 1/3 x 3.14 x 5x5x12
= 942/3
= 314 cu.cm.

24. VALUE :
Volume is the capacity of an object to hold , like that we
also have capacity to hold our anger and joy.

25. The height and the radius of a cone form a ______angle.
a) obtuse
b) acute
c) right

26. Volume of a cone =…………..
a) πr2
b) πr2h
c) 1/3πr2h

27. 1.find the volume of a cone of height 18 cm and a base
radius of 7 cm.
Here , r= ? and h= ?
a) 18 and 7
b) 7 and 18

28.  r =7 and h = 18
 Volume of a cone = 1/3πr2h
= 1/3 x 22/7 x 7 x 7 x18
= 1 x 22 x 7 x 6
= 22 x 42

29. hence , volume of a cone =……….
a) 448 cu. cm
b) 924 cu. cm
c) 846 cu.cm

31. Your answer is right.

33. Your answer is right.

35. Your answer is right.

37. Your answer is right.

39. Your answer is right.

41. Your answer is right.