A sphere,a cylinder and a cone are of same radius and same height and same radius. the ratio of their curved areas is
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1:3 is there curved areas
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Answer:
- Ratio is 4 : 4 : √5
Step-by-step explanation:
Given
- A sphere, a cylinder and a cone are of same radius and same height.
To find
- Ratio of their curved surface areas.
Solution
Let r be the common radius of a sphere, a cone and cylinder.
Then, height of sphere = its diameter = 2r
Then, height of cone = height of cylinder = height of sphere = 2r
Then, slant height of cone (l) = √r² + h²
- √r² + (2r)² = √r + 4r = √5r
S₁ = Curved surface area of sphere:
- 4πr²
S₂ = Curved surface area of cylinder:
- 2πrh = 2πr × 2r = 4πr²
S₃ = Curved surface area of cone:
- πrl = πr × √5r = √5πr²
∴ Ratio of curved surface area is:
S₁ : S₂ : S₃ = 4πr² : 4πr² : √5πr²
- 4 : 4 : √5
Hence, the ratio is 4 : 4 : √5
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