The radii of two cylinders are in the ratio 2 : 2 and their heights are in the ratio 5 : 3. Calculate the ratio of their columes and the ratio of their curved surfaces.
Answers
Given: The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3.
Ratio of radii of two cylinders = r1 : r2 = 2 : 3
Ratio of heights of two cylinders = h1 : h2 = 5 : 3
So, ratio of their volumes, V1 : V2 = π(r1)²h1 : π(r2)²h²
V1 : V2 = (r1)²h1 : (r2)²h2
V1 / V2 = (r1/r2)² × h1/h2
V1 / V2 = (2/3)² /(5/3)
V1 / V2 = (4/9) × 5/3
V1 / V2 = 20/27
V1 : V2 = 20 : 27
Ratio of their volumes = 20 : 27
Now, ratio of their curved surfaces :
Let the ratio of their curved surfaces of two cylinders be A1 and A2
A1/A2 = 2πr1h1/2πr2h2
A1/A2 = r1h1/r2h2
A1/A2 = r1/ r2 × h1/h2
A1/A2 = ⅔ × 5/3
A1/A2 = 10/9
A1 : A2 = 10 : 9
Ratio of their curved surfaces = 10 : 9
Hence, the ratio of their volume is 20 : 27 and the ratio of their curved surfaces is 10 : 9.
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