Question

7. Find the ratio of the curved surface area of
a sphere, a cylinder and a cone of the same
radius and same height
​

Answer 1

The ratio of the curved surface area of a sphere, a cylinder and a cone of same radius and same height is $\Righarrow 4:4:\sqrt{3}$

Step-by-step explanation:

Curved surface area of sphere $=4\pi r^2$

Curved surface area of cylinder$=2\pi rh$

Curved surface area of cone$=\pi rl$

let radius of sphere be x

height of cylinder = 2x

$l=\sqrt{4x^2-x^2}=x\sqrt{3}$

Ration of curved surface area of sphere, cylinder and cone

$\Rightarrow 4\pi r^2:2\pi rh:\pi rl$

$\Rightarrow 4\pi\cdot x^2:2\pi\cdot x\cdot 2x :\pi\cdot x\cdot x\sqrt{3}$

$\Rightarrow 4:2\cdot 2 :\sqrt{3}$

$\Rightarrow 4:4:\sqrt{3}$

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