Question

Hey !!

MENSURATION :

A sphere, a cylinder and a cone are of the same radius and same height. Find the ratio of their curved surface areas ?

No Copied Answers !!

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Answer 1

hey mate... ☜☆☞

here is ur answer... ^_^

the height of the sphere is the diameter the cone and cylinder have

$2r$

curved surface area of sphere

$4\pi {r}^{2}$

curved surface area of cylinder =

$2\pi {r}^{?} (2r)$

curved surface area of cone=

$\pi {r}l$

l = √(r2 + h2 ) = √( r2 + (2r)2) = √(5r2) = r√5

curvrd surface area of cone =

$\pi \sqrt{5r2}$

then..

ratio of curved surface area is a sphere cylinder and cone =

4πr2:2πrh : πrl

=4πr2:4πr2 : πr2√5

= 4 : 4 : √5

i hope its help u ☜☆☞

Answer 2

Here Is Your Ans ⤵

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Given :-

Height = Radius

To Find :-

CSA Of Sphere : CSA Of Cylinder : CSA Of Cone

Solution :-

➡CSA Of Sphere : CSA Of Cylinder : CSA Of Cone

➡4πR² : 2πRH : πRL

➡4πR² : 2πR² : πR $\sqrt{ {H }^{2} + { R }^{2} }$

➡4πR² : 2πR² : πR$\sqrt{ {R }^{2} + { R }^{2} }$

➡4πR² : 2πR² : πR$\sqrt{ {2R}^{2} }$

➡4πR² : 2πR² : πR × $\sqrt{2} \times \sqrt{ {(R)}^{2} }$

➡4πR² : 2πR² : πR²√2

➡4 : 2 : √2

➡2√2 : √2 : 1

Hence , CSA Of Sphere : CSA Of Cylinder : CSA Of Cone = $\fbox{2 \sqrt{2} }$ : $\fbox{ \sqrt{2} }$ : $\fbox{1}$

*****

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