Question

The volume of cylender is 308 cm!!
The radius of its base is 3.2 cm.
Find its curved surface area and
total surface area​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{C.S.A\:of\:cylinder=192.5\:cm^{2}}}}$

$\green{\tt{\therefore{T.S.A\:of\:cylinder=224.6536\:cm^{2}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Fiven:}} \\ \tt: \implies Volume \: of \: cylinder = 308 \: cm^{3} \\ \\ \tt: \implies Radius \: of \: cylinder = 3.2 \: cm \\ \\\red{\underline \bold{To \: Find:}}\\ \tt: \implies C.S.A \: of \: cylinder = ? \\ \\ \tt: \implies T.S.A \: of \: cylinder = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Volume \: of \: cylinder = 308 \: {cm}^{3} \\ \\ \tt: \implies {\pi r}^{2} h = 308 \\ \\ \tt: \implies h = \frac{308}{\pi {r}^{2} } \\ \\ \bold{as \: we \: know \: that} \\ \tt: \implies C.S.A\: of \: cylinder =2 \pi rh \\ \\ \tt: \implies C.S.A \: of \: cylinder =2\pi r \times \frac{308}{\pi {r}^{2} } \\ \\ \tt: \implies C.S.A \: of \: cylinder = 2\times\frac{308}{3.2} \\ \\ \green{\tt: \implies C.S.A \: of \: cylinder =192.5 { \: cm}^{2} } \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies T.S.A \: of \: cylinder = 2\pi r(h + r) \\ \\ \tt: \implies T.S.A\: of \: cylinder =2\pi r( \frac{308}{\pi {r}^{2} } + r) \\ \\ \tt: \implies T.S.A\: of \: cylinder =2\pi r \times( \frac{308 + \pi{r}^{3} }{ \pi{r}^{2} } ) \\ \\ \tt: \implies T.S.A \: of \: cylinder = \frac{616 + 2\pi {r}^{3}}{r} \\ \\\tt: \implies T.S.A \: of \: cylinder = \frac{616 + 2 \times 3.14 \times {(3.2)}^{2} }{3.2} \\ \\ \tt: \implies T.S.A \: of \: cylinder = \frac{718.89152}{3.2} \\ \\ \green{\tt: \implies T.S.A\: of \: cylinder =224.6536 { \: cm}^{2} }$

Answer 2

$</p><p>\tt{\pink{\purple{Hello!!! }}}$

$</p><p>\huge{\boxed{\boxed{\green{\bullet{Question \: - }}}}}$

The volume of cylender is 308 cm!!

The radius of its base is 3.2 cm.

Find its curved surface area and total surface area.

$</p><p>\huge{\boxed{\boxed{\red{\bullet{Solution \: - }}}}}$

$</p><p>\tt{\orange {Step-By-Step-Explaination \: : }}$

$</p><p>\tt{\red{Given \: - }}$

• The volume of cylinder is 308 cm.

• The radius of its base is 3.2 cm.

_________

$</p><p>\tt{\purple{Volume \: Of \: A \: Cylinder = \pi {r}^2 h = 308 }}$

$</p><p>\tt{\red{\therefore{Height \: = \dfrac{308}{\pi {r}^2 } }}}$

We Know That :

$\tt{ \orange{C.S.A \: = \: 2 \:\pi \: r \: h \: = 2\pi \: r \: \times \dfrac{308}{\pi \: {r}^{2} \: } = 192.5 \: {cm}^{2} }}$

$\tt { \blue{T.S.A \: = 2\pi \: r(h + r) = \: 224.6536 \:{cm}^2 }}$