If the height and the radius of a cone is trippled.then find the ratio of volume of new cone to that of original cone.

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Solution

Dear Student,

$L e t t h e o r i g i n a l r a d i u s o f b a s e o f c o n e = r L e t t h e o r i g i n a l h e i g h t o f c o n e = h O r i g i n a l v o l u m e o f c o n e = V = \frac{1}{3} π r^{2} h N e w r a d i u s o f b a s e o f c o n e = r_{1} = 3 r N e w h e i g h t o f c o n e = h_{1} = 3 h N e w v o l u m e = V_{1} = \frac{1}{3} π {r_{1}}^{2} h_{1} = \frac{1}{3} π (3 r)^{2} 3 h = \frac{1}{3} π \times 9 r^{2} \times 3 h = 27 \times \frac{1}{3} π r^{2} h N o w, \frac{V_{1}}{V} = \frac{27 \times \frac{1}{3} π r^{2} h}{\frac{1}{3} π r^{2} h} = \frac{27}{1} = 27 : 1$
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