The radii of 2 cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. Calculate the ratio of their curved surfaces.
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The radii of 2 cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. Calculate the ratio of their
Answer:
Ratio of their curved surfaces is 10:9
Step-by-step explanation:
Curved surface of the cylinder is 2πrh
Curved surface for first cylinder is 2π x 2 x 5 = 20π
Curved surface for second cylinder is 2π x 3 x 3 = 18π
Ratio of their curved surfaces. is = 20 π : 18 π = 10: 9
Hence the ratio is 10: 9
Verified answer
Answer:
The ratio of their curved surface is 10 : 9
Step-by-step explanation:
Given as :
The radius of two cylinder are in ratio 2 : 3
i. radius are 2 x , 3 x
The height of two cylinder are in ratio 5 : 3
i.e height are 5 y , 3 y
Since curved surface area of cylinder = 2 × π × r × h
where r is radius
and h is height
So, the ratio of curved surface area
[tex]\dfrac{curved surface of cylinder _1}{curved surface of cylinder _2}[/tex] = [tex]\dfrac{2 \pi r_1 h_1}{2 \pi r_2 h_2 }[/tex]
i.e [tex]\dfrac{curved surface of cylinder _1}{curved surface of cylinder _2}[/tex] = [tex]\dfrac{2 \Pi \times 2 x \times 5 y}{2 \times \Pi \times 3 x\times 3 y}[/tex]
Or, [tex]\dfrac{curved surface of cylinder _1}{curved surface of cylinder _2}[/tex] = [tex]\dfrac{10}{9}[/tex]
So, the ratio of [tex]\dfrac{curved surface of cylinder _1}{curved surface of cylinder _2}[/tex] = [tex]\dfrac{10}{9}[/tex]
Hence, The ratio of their curved surface is 10 : 9 Answer