Question

Find the curved surface area of a cylinder given its base circumference is 36 cm and its height is 4 cm.
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Answer 1

AnswEr-:

• $\underline{\mathrm {\bf{\dag{ \pink{Curved\:Surface\:Area\:or\:C.S.A \:of\:Cylinder\:= 143.68 \: cm^{2} \: [ Approx] }}}}}$

Explanation-:

• $\mathrm{\bf{\blue {Given \:\: -:}}} \begin{cases} \sf{\blue{The\:Circumference \:of\:the\:base \:of\:Cylinder \:is\:= \frak{36\:cm}}} & \\\\ \sf{\red{Height \:of\:Cylinder \:is \:=\:\frak{4cm}}}\end{cases}$

• $\mathrm{\bf{\blue {To \:Find\: -:}}} \begin{cases} \sf{\blue{The\:Curved\:Surface \:Area\:of\:the\: \:of\:Cylinder }}\end{cases}$

$\mathrm {\bf{\dag{ Solution \:of\:Question \:-:}}}$

• First of all we need to find the Radius of the Cylinder's baee by putting the known Values in the Formula for Circumference of Circle .

$\mathrm {\bf{\dag{Finding \:Radius \: of\:Cylinder's\:base\:-:}}}$

As , We know that ,

• $\underline{\boxed {\red{\dag{\mathrm {Circumference _{( Circle)} = 2 \times \pi \times Radius\:units}}}}}$

• $\mathrm{\bf{\blue {Here \:\: -:}}} \begin{cases} \sf{\blue{The\:Circumference \:of\:the\:base \:of\:Cylinder \:is\:= \frak{36\:cm}}} & \\\\ \sf{\red{Radius \:of\:Cylinder's\:base \:is \:=\:\frak{??}}}& \\\\ \sf{\pink{ \pi \:=\:\frak{\dfrac{22}{7}}}}\end{cases}$

Now , By Putting known Values in Formula for Circumference for Circle-:

• $\longmapsto {\mathrm {36\:cm= 2 \times \dfrac{22}{7} \times Radius }}$
• $\longmapsto {\mathrm {36\:cm= \dfrac{44}{7} \times Radius }}$
• $\longmapsto {\mathrm {\dfrac{36\times 7}{44}\:= Radius }}$
• $\longmapsto {\mathrm {\dfrac{\cancel {252}}{\cancel {44}}\:= Radius }}$
• $\underline {\boxed{\mathrm {Radius\:=5.72cm\: }}}$

Therefore,

• $\underline{\mathrm {\bf{\dag{ \pink{Radius \:of\:Cylinder's \: Base \:-:5.72\:cm}}}}}$

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$\mathrm {\bf{\dag{Finding \:Curved \:Surface \:Area\: of\:Cylinder\:-:}}}$

• $\underline{\boxed {\red{\dag{\mathrm {Curved \:Surface \:Area_{( Cylinder)} = 2 \times \pi \times Radius\times Height\:sq.units}}}}}$

• $\mathrm{\bf{\blue {Here \:\: -:}}} \begin{cases} \sf{\blue{The\:Radius \:of\:the\:base \:of\:Cylinder \:is\:= \frak{5.72\:cm}}} & \\\\ \sf{\red{Height \:of\:Cylinder\: \:is \:=\:\frak{4cm}}}& \\\\ \sf{\pink{ \pi \:=\:\frak{\dfrac{22}{7}}}}\end{cases}$

• Now , By Putting known Values in Formula for Curved surface area for Cylinder -:

• $\longmapsto {\mathrm {C.S.A \:= 2 \times \dfrac{22}{7} \times 5.72 \times 4 }}$
• $\longmapsto {\mathrm {C.S.A \:= \dfrac{44}{7} \times 5.72 \times 4 }}$
• $\longmapsto {\mathrm {C.S.A \:= \dfrac{44}{7} \times 22.88 }}$
• $\longmapsto {\mathrm {C.S.A \:= \dfrac{\cancel {44}}{\cancel {7}} \times 22.88 }}$
• $\longmapsto {\mathrm {C.S.A \:= 6.28 \times 22.88 }}$
• $\underline { \boxed{\mathrm {C.S.A \:= 143.68 \: cm^{2} \: [ Approx] }}}$

Hence,

• $\underline{\mathrm {\bf{\dag{ \pink{Curved\:Surface\:Area\:or\:C.S.A \:of\:Cylinder\:= 143.68 \: cm^{2} \: [ Approx] }}}}}$

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Answer 2

Answer:

QUESTION

Find the curved surface area of a cylinder given its base circumference is 36 cm and its height is 4 cm.

ANSWER

$\fbox \green{first \: we \: will \: find \: radius} \\ \\ \red {36 \times 2 \times \frac{22}{7} \times r} \\ \\ \red {36 \times \frac{44}{7}r} \\ \\ \red {r = \frac{252}{44}} \\ \\ \pink { = r = 5.72cm} \\ \\ \\ \fbox \green{now \: we \: will \: find \: the \: of \: curved \: surface \: area \: of \:cylinder} \\ \\ \blue{2 \times \frac{22}{7} \times 5.72 \times 4} \\ \\ \blue{ \frac{44}{7} \times 22.88} \\ \\ \blue {6.285 \times 22.88} \\ \\ \orange { = 143.817}$

I hope it helps you

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