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प्रश्न
The radius of two right circular cylinder are in the ratio of 2 : 3 and their heights are in the ratio of 5: 4 calculate the ratio of their curved surface areas and also the ratio of their volumes.
उत्तर
Let the radii of two cylinders be 2r and 3r respectively and their heights be 5h and 4h respectively.
Let S1 and S2 be Curved Surface Area of the two cylinders and V1 and V2 be their volumes.
Then, S1 = Curved surface area of the cylinders of height 5h and radius 2r.
⇒ 2π x 2r x 5h = 20πrh sq. units.
S2 = Curved surface area of the cylinders of height 4h and radius 3r.
⇒ 2π x 3r x 4h = 24πrh sq. units.
`S_1/S_2 = (20πrh)/(24πrh) = 5/6`
S1: S2 = 5: 6
V1 = Volume of cylinder of height 5h and radius 2r
= π x (2r)2 x 5h = 20πr2h cubic units.
V2 = Volume of the cylinder of height 4h and radius 3r.
= π x (3r)2 x 4h = 36πr2h cubic units.
∴ `V_1/V_2 = (20πr^2h)/(36πr^2h) = 5/6`
V1: V2 = 5: 9.
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