The height of two cylinders are in the ratio 5 ratio 3 ratio and the volume of cylinders are in the ratio 20 ratio 27 ratio find the ratio of theri radius
Answers
Ratio of their radius = First Cylinder : Radius of Second Cylinder = 2 : 3
Step-by-step explanation:
Let,
Height of First Cylinder = 5a
Height of Second Cylinder = 3a
Π (Radius of First Cylinder)^2 x (Height of First Cylinder) / Π (Radius of Second Cylinder)^2 x (Height of Second Cylinder) = 20/27
(Radius of First Cylinder)^2 x 5a/ (Radius of Second Cylinder)^2 x 3a = 20/27
(Radius of First Cylinder)^2 x 5/ (Radius of Second Cylinder)^2 x 3 = 20/27
(Radius of First Cylinder)^2 / (Radius of Second Cylinder)^2 = 20 x 3/27 x 5
(Radius of First Cylinder)^2 / (Radius of Second Cylinder)^2 = 20 x 3/27 x 5
= 4 / 9
(Radius of First Cylinder) / (Radius of Second Cylinder) = sqrt (4/9)
(Radius of First Cylinder) / (Radius of Second Cylinder) = 2 / 3
So,
Ratio of their radius = First Cylinder : Radius of Second Cylinder = 2 : 3
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