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VOLUMES OF RIGHT CIRCULAR CYLINDER & CONE CLASS-VIII PRESENTED BY MAHESH KUMAR BADETRI TGT (MATHS) JAWAHAR NAVODAYA VIDYALAYA DURG

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OBJECTIVES After completion of this presentation you will be able to know about:- The basic knowledge of cone and cylinder. How to calculate the volume of cone and cylinder. How to solve the problems of cone & cylinder.

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PREVIOUS KNOWLEDGE SSSStudents must have knowledge of s s s shapes of circle & its area rrrright angle triangle rrrrectangle etc.

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CONTENTS IIIIntroduction SSSSome examples of cylinder & cone FFFFormulas for evaluation of volume of cylinder and cone AAAAn ideal problem and solutions of that problem RRRRecapitulation QQQQuery session. AAAAssignment. AAAAcknowledgement.

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CYLINDER

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Base of the cylinder * Base of a cylinder is a circle So that the area of the base = π r2 r O

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DISCRIPTION A right circular cylinder is made of many circular discs

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3-D FORM

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When a rectangle rotates through any side,it becomes a right circular cylinder.

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FORMULA VVVVolume of the cylinder = Area of the base X height V = π r2 x h

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IDEAL QUESTION Ques. :-The diameter of the base of a right circular cylinder is 7 cm. and its height is 40 cm. Find the volume of the cylinder ? Sol. :- Here diameter = 7 cm. radius r = 7/2 cm. height h = 40 cm. So the volume of cylinder V = π r2h V = 22/7x (7/2)2x 40 V = 22/7x 7/2x7/2x 40 V = 1540 cm3

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When we rotate a right angle triangle through its perpendicular or base, a right circular cone appears A B C

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RIGHT CIRCULAR CONE

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1/3 π r2h 1/3 π r2h 1/3 π r2h π r 2 h π r 2 h

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Hence a right circular cylinder is made of three equal right circular cones. So volume of a right circular cone = 1/3 ( volume of right circular cylinder) = 1/3 ( volume of right circular cylinder) V = 1/3 x π r 2 h V = 1/3 x π r 2 h

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RECAPITULATION A cylinder is made of circular discs When a rectangle rotates through any side, it becomes a cylinder. When a right angle triangle rotates through any of its perpendicular sides, forms a cone. Volume of cylinder = π r 2 h Volume of cone =1/3 π r 2 h

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IDEAL QUESTION FFFFind the volume of a right circular cone whose height is 2.04 m and the radius of the base is 14 cm. SSSSol.:- Here radius r = 14 cm. height h =2.04m. = 204 cm. So the volume of cone V = 1/3 π r2h V = 1/3X 22/7x14x14x204 V = 41888 cm3

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