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# Cai12 m120volume and surface areaviii

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### Cai12 m120volume and surface areaviii

1. 1. SUBJECT: MATHSPRESENTED BY : MONA A. PATILROLL NO.: 68YEAR: 2011-2012
2. 2. CONTENTSCONEVOLUME OF CONE
3. 3. INTRODUCTION In previous class we have studied about volume andsurface area of a cylinder.
4. 4.  What do we called this shape?a) Triangleb) Conec) Cylinder
5. 5. Today we are going to studyabout the volume of a Cone.
6. 6.  A cone has one circular flat surface and one curvedsurface.
7. 7.  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.
8. 8. In diagram alongside ∠A = 90̊AOP
9. 9. BAC
10. 10. ∴The angle between the height of the cone and aradius of the base is a right angle.
11. 11. The measure of the space occupied by any cone iscalled volume of the Cone.
12. 12. Volume of a Cone =1/3 x area of base x height.
13. 13. Base of a Cone is a circle.What is the area of a circle?a) πr2b) 2πrc) πd
14. 14.  Area of base = πr2∴ volume of a cone = 1/3 xπr2x h= 1/3 πr2h
15. 15. 1. The height of a cone is 14cm and the radius of its base is3cm. What is its volume?Solution : Here, r= 3cm, h= 14cmVolume of cone = 1/3πr2h= 1/3x 22/7 x 3x3 x14= 22x 3 x9= 132 cu.cm
16. 16. 2. Find the volume of a cone of height 7cm and a base radiusof 9cm.Solution: Here, r = 9cm , h = 7cmVolume of Cone = 1/3πr2h= 1/3 x 22/7 x 9 x 9 x 7= 22 x 3 x9= 594 cu. cm
17. 17. 3.The radius of the base of a cone is 5cm and it’s slantheight is 13cm. Find the volume of thecone.(π=3.14)Solution: here r=5cm, l=13cmTo find out the volume of the cone we require height(h)of the cone.
18. 18. The height and the radius of a cone form a rightangle.So we will use ‘Pythagoras’ theorem to find out heheight of the cone.
19. 19. Using Pythagoras theoreml2 = r2 + h2∴ 132 = 52 + h2∴ h2 = 132 – 52∴ h2 = 169– 25∴ h2 = 144∴ h = 12
20. 20. Volume of a cone = 1/3πr2h= 1/3 x 3.14 x 5x5x12= 942/3= 314 cu.cm.
21. 21. VALUE :Volume is the capacity of an object to hold , like that wealso have capacity to hold our anger and joy.
22. 22. The height and the radius of a cone form a ______angle.a) obtuseb) acutec) right
23. 23. Volume of a cone =…………..a) πr2b) πr2hc) 1/3πr2h
24. 24. 1.find the volume of a cone of height 18 cm and a baseradius of 7 cm.Here , r= ? and h= ?a) 18 and 7b) 7 and 18
25. 25.  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
26. 26. hence , volume of a cone =……….a) 448 cu. cmb) 924 cu. cmc) 846 cu.cm