Question
A cone is cut parallel to its base in 3 parts in such a
way that the height of each part is same. Find the ratio of volume of these parts?Solution
Volume of cone ABC = 1/3 π(r1)2 h ............(1) Volume of Frustrum BCED = 1/3 π(2r1)2 2h - 1/3 π(r1)2 h = 7/3 π(r1)2 h ............(2) Volume of Frustrum DEGF = 1/3 π(3r1)2 3h - 1/3 π(2r1)2 2h = 19/3 π(r1)2 h ............(3) Now, ratio = 1/3 π(r1)2 h : 7/3 π(r1)2 h : 19/3 π(r1)2 h = 1:7:19
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