Question
If both the radius and height of a right circular cone are increased by 20 % , its volume will be increased by :
Answer: Option D
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Let the original radius and height of the cone be r and h respectively .
Then , original volume = `1/3 pi r^2 h`
New radius = `120/100 r = 6/5 r, New height = 6/5 h`
New volume = `1/3 pi xx (6/5 r)^2 xx (6/5 h) = 216/125 xx 1/3 pi r^2 h`
Increase in volume = `91/125 xx 1/3 pi r^2 h`
`:.` Increase % = `((91/125 xx 1/3 pi r^2 h)/(1/3 pi r^2 h) xx 100)%` = 72.8%
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