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, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 5 years, 5 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 {tex}= 2r{/tex}
Let 'l’ be the slant height of the cone. Then
{tex}l ={/tex} {tex}\sqrt{r^2 + h^2}{/tex}= {tex}\sqrt{r^2 + (2r)^2}{/tex} = {tex}\sqrt{5}{/tex}r
{tex}S_1 ={/tex} Curved surface area of cylinder {tex}= 2\pi rh{/tex}
{tex}= 2\pi r . 2r = 4\pi r^2{/tex}
{tex}S_2 ={/tex} Curved surface area of cone = {tex}\pi{/tex}{tex}rl ={/tex} {tex}\pi{/tex}r{tex}\sqrt{5}{/tex}{tex}r = {/tex}{tex}\sqrt{5}{/tex}{tex}\pi{/tex}{tex}r^2 {/tex}
{tex}S_3={/tex} Curved surface area of sphere {tex}= 4\pi r^2{/tex}
{tex}S_1 : S_2 : S_3 = 4\pi r^2 :\sqrt5\pi r^2 : 4\pi r^2{/tex}
{tex}\therefore{/tex}{tex}S_1 : S_2 : S_3 = 4 :\sqrt5 : 4{/tex}

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CBSE > Class 09 > Mathematics