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Question
If the radius of the base of a cone is halved, keeping the height same, what is the ratio of the volume of the reduced cone to that of the original cone?
Solution
Let radius of cone is r and height is h
Volume `V1=1/3pir^2h `
In another case,
Radius of cone = half of radius =` r/2`
Height =h
∴ `Volume= (V_2)=1/3pi(1/2r)^2h`
=` 1/3pixxr^2/4xxh`
= `1/12pir^2h`
∴ `V_1/V_2=(1/12pir^2h)/(1/3pir^2h)=3/12=1/4`
∴ Ratio will be (1:4).
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