Question

Example 9. A right circular
cylinder just encloses a sphere of
radius r. Find
(i) surface area of the sphere,
(ii) curved surface area of the
cylinder,
(iii) ratio of the areas obtained in (i) and (ii).

Quanlity ans required!​

Answer 1

i) Radius = r

Surface area of sphere = 4πr²

ii) Curved surface area of cylinder = 2πrh

Radius of cylinder = r

height of cylinder = r + r = 2r

Curved surface area of cylinder = 2πrh

= 2πr(2r)

= 4πr²

$iii ) Ratio = \frac{Surface \: area \: of \: sphere \: obtained \: in \: (i)}{Surface \: area \: of \: cylinder \: obtained \: in \: (ii)}$

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

$= \frac{1}{1}$

= 1:1

keep smiling ❣️

good night

salty dreams

Answer 2

$\Large{\underline{\underline{\bf{Required\:Answer:}}}}$

$\implies{\boxed{\sf{\blue{(i)4\pi r^{2}}}}}$

$\implies{\boxed{\sf{\blue{(ii)4\pi r^{2}}}}}$

$\implies{\boxed{\sf{\blue{(iii)1\: : 1\:.}}}}$

$\Large{\underline{\underline{\bf{Explanation:}}}}$

(i) $\displaystyle{\sf{Surface\:area\:of\:the\:sphere\:=\:4 \pi r^{2}}}$

(ii) For Cylinder

Radius of the base = r

Height = 2r

${\therefore}$ Curved surface area of the cylinder

:$\implies{\sf{2 \pi(r)(2r) = 4\pi r^{2}}}$

(iii) Ratio of the areas obtained in (i)and(ii)

$\displaystyle{\sf{= \frac{Surface\:area\:of\:the\:sphere}{Curved\:surface\:area\:of\:the\:cylinder}}}$

$\displaystyle{\sf{= \dfrac{4\pi r^{2}}{4 \pi r^{2}}\:=\: \dfrac{1}{1}\:=\: 1:1.}}$

__________________________