A sphere,cylinder and cone are of …

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A sphere,cylinder and cone are of same radius and same height.Find the ratio of their curved surfaces.

Posted by Diya Garg 5 years, 10 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 5 years, 10 months ago

Suppose r be the common radius of a cylinder, cone and a sphere.
height of the cylinder = Height of the cone = Height of the sphere $= 2r$
Let 'l’ be the slant height of the cone. Then
$l =$ $\sqrt{r^2 + h^2}$ = $\sqrt{r^2 + (2r)^2}$ = $\sqrt{5}$ r
$S_1 =$ Curved surface area of cylinder $= 2\pi rh$
$= 2\pi r . 2r = 4\pi r^2$
$S_2 =$ Curved surface area of cone = $\pi$ $rl =$ $\pi$ r $\sqrt{5}$ $r =$ $\sqrt{5}$ $\pi$ $r^2$
$S_3=$ Curved surface area of sphere $= 4\pi r^2$
$S_1 : S_2 : S_3 = 4\pi r^2 :\sqrt5\pi r^2 : 4\pi r^2$
$\therefore$ $S_1 : S_2 : S_3 = 4 :\sqrt5 : 4$

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