Question

what is the ratio of curved surface rea of the cylender and surface area of sphere​

Answer 1

TO FIND :-

• The ratio of CSA of Cylinder and Surface area of sphere.

FORMULAE USED :-

• CSA of cylinder = 2πrh.
• surface area of sphere = 4πr².

SOLUTION :-

$\\ : \implies \displaystyle \sf \: \frac{CSA \: of \: Cylinder}{Surface \: area \: of \: Sphere} = \frac{2\pi rh}{4\pi r ^{2} }$

$: \implies \displaystyle \sf \: \frac{CSA \: of \: Cylinder}{Surface \: area \: of \: Sphere} = \frac{2\pi rh}{4\pi r \times r}$

$: \implies \displaystyle \sf \: \frac{CSA \: of \: Cylinder}{Surface \: area \: of \: Sphere} = \frac{h}{2r}$

$: \implies \underline{ \boxed{ \displaystyle \sf \: CSA \: of \: Cylinder \: : \: Surface \: area \: of \: Sphere = h \: : \: 2r}}$

Hence The ratio of CSA of Cylinder and Surface area of sphere is h : 2r.

Answer 2

Find:

• Ratio of curved surface area of Cylinder and Surface Area of Sphere

Solution:

we, know that

$\boxed{\sf Curved \: surface \: area \: of \: cylinder = 2 \pi rh}$

And,

$\boxed{\sf surface \: area \: of \: sphere = 4 \pi {r}^{2} }$

So,

$\heartsuit \sf Ratio = \dfrac{curved \: surface \: area \: of \: cylinder}{surface \: area \: of \: sphere} \\ \\ \\ \dashrightarrow \sf Ratio = \dfrac{2 \pi rh}{4 \pi {r}^{2} } \\ \\ \\ \dashrightarrow \sf Ratio = \dfrac{rh}{2{r}^{2} }\\ \\ \\ \dashrightarrow \sf Ratio = \dfrac{rh}{2{r}^{2} }\\ \\ \\ \dashrightarrow \sf Ratio = \dfrac{rh}{2r \times r}\\ \\ \\ \dashrightarrow \sf Ratio = \dfrac{h}{2r}$

Hence, Ratio of Curved surface area of Cylinder and Surface Area of Sphere = h : 2r

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$\qquad \bf{Additional \: Info.}$

$\begin{lgathered} \boxed{\begin{minipage}{8.7cm} \bf \boxed{1} Curved\:surface\:area\:of\:cuboid =2(l + b)h \\ \\ \bf \boxed{2} Curved\:surface\:area\:of\:cube =4{a}^{2} \\ \\ \bf \boxed{3} Curved \: surface \: area \: of \: cylinder =2\pi rh \\ \\ \bf \boxed{4} Curved \: surface \: area \: of \: cone = \pi rl \\ \\ \bf \boxed{5} Curved \: surface \: area \: of \:hemisphere =2 \pi {r}^{2} \\ \rule{250}{2} \\ \bf \boxed{1} Surface \: area \: of \: cuboid =2(lb + bh + hl) \\ \\\bf \boxed{2} Surface \: area \: of \: cube =6 {a}^{2} \\ \\ \bf \boxed{3} Surface \: area \: of \: cylinder =2 \pi r(r + h) \\ \\ \bf \boxed{4} Surface \: area \: of \: cone = \pi r(l + r) \\ \\ \bf \boxed{5} Surface \: area \: of \: sphere=4 \pi {r}^{2} \\ \\ \bf \boxed{6} Surface \: area \: of \: hemisphere =3 \pi {r}^{2} \end{minipage}}\end{lgathered}$