Question

the circumference of the base of cylinder is 30.8cm.Its curved surface area is 289.52.find the height of cylinder​

Answer 1

Given :

• Circumference of the base of Cylinder is 30.8 cm .
• Curved Surface is 289.52 cm .

To Find :

• Height of Cylinder .

Solution :

Firstly we'll find the Radius of Cylinder :

Using Formula :

$\longmapsto\tt\boxed{Circumference\:of\:Cylinder=2\pi{r}}$

Putting Values :

$\longmapsto\tt{30.8=2\times\dfrac{22}{7}\times{r}}$

$\longmapsto\tt{30.8\times{7}=44\:r}$

$\longmapsto\tt{215.6=44\:r}$

$\longmapsto\tt{r=\cancel\dfrac{215.6}{44}}$

$\longmapsto\tt\bf{r=5\:cm(Approx.)}$

Now ,

For Height :

Using Formula :

$\longmapsto\tt\boxed{C.S.A\:of\:Cylinder=2\pi{rh}}$

Putting Values :

$\longmapsto\tt{289.52=2\times\dfrac{22}{7}\times{5}\times{h}}$

$\longmapsto\tt{289.52\times{7}=44\times{5h}}$

$\longmapsto\tt{2026.64=220\:h}$

$\longmapsto\tt\bf{h=9.21\:(Approx.)}$

Answer 2

Given :-

• circumference of base=30.8cm
• CSA of given cylinder is 289.52cm

${}$

${\large{\underline{\pink{\sf{To\:Find\: :-}}}}}$

• Height of Cylinder=?

$\begin{gathered} \\ \qquad{\rule{200pt}{2pt}} \end{gathered}$

$\:\: \Large{\maltese{\underline{\underline{\gray{\sf{Solution\: :-}}}}}}$

${}$

Formula Using

$\boxed{\begin{array}{ccc} \longmapsto \sf Circumference_{\:Circle}=2 \pi rh \\ \\ \longmapsto \sf CSA_{\:Cylinder}=2\pi rh \end{array}}$

$\:\: \large{\bigstar{\underline{\underline{\sf{Calculation\: :-}}}}}$

${}$

$\begin{gathered} \\ \qquad{\rule{200pt}{2pt}} \end{gathered}$

Calculating radius

${\dashrightarrow{\sf{\qquad Circumference=2\pi r}}}$

Putting Values...

${\dashrightarrow{\sf{\qquad 30.8=2\times \dfrac{22}{7} r}}}$

${\dashrightarrow{\sf{\qquad 44r=7 \times 30.8}}}$

${\dashrightarrow{\sf{\qquad 44r=215.6}}}$

${\dashrightarrow{\sf{\qquad r= \dfrac{215.6}{44}}}}$

${\dashrightarrow{\sf{\qquad r= \cancel\dfrac{215.6}{44}=5}}}$

${\rightsquigarrow{\qquad{\:\:\:\: {\underline{\boxed{\sf{radius\:of\:cylinder=5cm(approx)}}}}}}}$

$\begin{gathered} \\ \qquad{\rule{200pt}{2pt}} \end{gathered}$

${}$

Calculating Height

${\dashrightarrow{\sf{\qquad CSA=2\pi rh}}}$

Putting Values ...

${\dashrightarrow{\sf{\qquad 289.52=2\times \dfrac{22}{7} \times 5 \times h }}}$

${\dashrightarrow{\sf{\qquad 7 \times 289.52=220h}}}$

${\dashrightarrow{\sf{\qquad h=\dfrac{2026.64}{220}}}}$

${\dashrightarrow{\sf{\qquad h=\cancel\dfrac{2026.64}{220}=9.21}}}$

${\rightsquigarrow{\qquad{\:\:\:\: {\underline{\boxed{\sf{height\:of\:cylinder=\red{9.21cm(approx)}}}}}}}}$

$\begin{gathered} \\ {\rule{200pt}{2pt}} \end{gathered}$

${\therefore}$Approximately height of given Cylinder is 9.21 cm

$\begin{gathered} \\ {\underline{\rule{200pt}{7pt}}} \end{gathered}$