If the radius of the base of a cone is doubled keeping the height same. What is the ratio of the volume of the larger cone to the smaller cone?

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Prachi Dhamdhere

When we take height=h and radios of base=r then volume of cone=?r^2*h/3 if radios of the base is doubled then R=2r and height=h so, volume is =?(2r)^2*h/3 therefore, ratio of the volume of latter cone to the smaller cone = ?r^2*h/3/?(2r)^2*h/3 =r^2/4r^2 =1/4 =1:4 Answer
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Given: Smaller cone's radius 'r' Larger cone's radius '2r' W.K.T: Volume of cone =1/3 * pi* r^2 * h ----? A Therefore, volume of larger cone = 1/3 * pi * (2r)^2 * h =4/3 * pi * r^2 *h ----? B To Find: Volume of larger cone : vol of smaller Which is B : A as labelled...
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Given: Smaller cone's radius 'r' Larger cone's radius '2r' W.K.T: Volume of cone =1/3 * pi* r^2 * h ----? A Therefore, volume of larger cone = 1/3 * pi * (2r)^2 * h =4/3 * pi * r^2 *h ----? B To Find: Volume of larger cone : vol of smaller Which is B : A as labelled above Therefore 4:1 Hence the solution! read less
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Let the radius, height of small cone & large cone be r, R and h (since height is same) respectively. Given that R=2r Volume is given by v=pi*(r^2)*h/3. Let VL & VS be volumes of large and small cones respectively. therefore, VL/VS=(R^2)/(r^2)=4/1. Hence required ratio is 4:1
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Formula for the volume of a cone is 1/3 pi r^2 h so assuming in one case the radius is R and in another case the radius is 2R, we get the desired ratio = (1/3 pi (2R)^2 h) / (1/3 pi (R)^2 h) = 4 Ans
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When we take height=h and radios of base=r then volume of cone=?r^2h/3 if radios of the base is doubled then R=2r and height=h so, volume is =?(2r)^2h/3 therefore, ratio of the volume of latter cone to the smaller cone = ?r^2h/3/?(2r)^2h/3 =r^2/4r^2 =1/4 =1:4 Answer
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