the ratio of radii of two clyinders 1:2 and the hieghtly are in ratio 2:3 find the ratio of their vloume
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Therefore, the ratio of their volume is 1/6. The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio of 5 : 3.
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Let the radii of the two cylinders be r and R respectively and the heights of the two cylinders be h and H respectively.
Ratio of Radii of cylinders = 1:2 = r:R
Therefore, r = R/2.
Ratio of the Heights of cylinders = 2:3 = h:H
Therefore, 3h = 2H
h = 2H/3.
Ratio of the Volumes = 2πr²h:2πR²H
= r²h:R²H
= (R/2)²×(2H/3) : R²H
= (R²/4)×2H/3 : R²H
= 2R²H/12 : R²H
= R²H/6 : R²H
= 1/6:1
= 1:6
The Ratio of the Volumes of the Cylinders is 1:6.
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