Question

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

Answer 1

Given -

• Circumference of base is 36 cm

• Height of cylinder is 4 cm

To find -

• Curved surface area of cylinder.

Formula used -

• CSA of Cylinder.

Solution -

In the question, we are provided with the circumference of base of the cylinder and the height of the cylinder. So, first we will find the radius of the cylinder, from the formula of circumference of the base, after that, we will curved surface area of cylinder.

According to question -

• Circumference of base, c = 36 cm

• Radius of cylinder = r

• Value of pie, π = $\bf\frac{22}{7}$

Circumference of base -

• $\bf 2\pi r$

On substituting the values -

$\bf \longrightarrow \: c \: = 2\pi r \\ \\ \bf \longrightarrow \: 36 \: cm \: = 2 \: \times \dfrac{22}{7} \: \times \: r \\ \\ \bf \longrightarrow \: 36 \: cm \: = \dfrac{44}{7} \: \times \: r \\ \\ \bf \longrightarrow \: 36 \: cm \: = 6.2 \: \times \: r \\ \\ \bf \longrightarrow \: r \: = \dfrac{36}{6.2} \\ \\ \bf \longrightarrow \: r \: = 5.8 \: cm$

Now -

• Radius, r = 5.8 cm

• Height, h = 4 cm

• Curved surface area = CSA

Curved surface area -

• $\bf 2\pi rh$

On substituting the values -

$\bf \longrightarrow \: CSA \: = 2\pi rh \\ \\ \bf \longrightarrow \: CSA \: = \: 2 \: \times \dfrac{22}{ \cancel{7}} \: \times \cancel{5.8 }\: cm \: \times 4 \: cm \\ \\ \bf \longrightarrow \: CSA \: = 2 \: \times 22 \: \times 0.8 \: cm \: \times 4 \: cm \\ \\ \bf \longrightarrow \: CSA \: = 140.8 \: { \: cm}^{2}$

$\therefore$ The curved surface area of Cylinder is 140.8 cm²

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Answer 2

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${\large{\bold{\rm{\underline{Let's \; understand \; the \; question \; .1^{st}}}}}}$

★ This question says that we have to find the curved surface area of a cylinder and it is already given that it's base circumference is 36 cm and it's height is 4 cm. Means base circumference is in circular shape. Let's do it !..

${\large{\bold{\rm{\underline{Given \; that}}}}}$

★ Base circumference of cylinder = 36 cm

★ Height of cylinder = 4 cm

${\large{\bold{\rm{\underline{To \; find}}}}}$

★ The curved surface area of a cylinder

${\large{\bold{\rm{\underline{Solution}}}}}$

★ The curved surface area of a cylinder = 140.8 cm²

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${\large{\bold{\rm{\underline{Using \; concepts}}}}}$

★ Formula to find circumference of the base that is in shape of circle.

★ Formula to find Curved Surface Area of cylinder.

${\large{\bold{\rm{\underline{Using \; formulas}}}}}$

★ C (circular in shape) = 2πr

★ CSA (cylinder) = 2πrh

${\large{\bold{\rm{\underline{Where,}}}}}$

★ C denotes circumference

★ π is pronounced as pi

★ The value of π is 22/7 or 3.14

★ r denotes radius

★ CSA dentoes curved surface area

★ h denotes height

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${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

✠ Firstly let us find the radius of this cylinder..!

➙ C = 2πr

➙ 36 = 2(3.14)(r)

➙ 36 = 2 × 3.14 × r

➙ 36 = 6.28 × r

➙ 36/6.28 = r

➙ 5.8 = r

➙ r = 5.8 cm (approx)

${\frak{Henceforth, \: 5.8 \: cm \: is \: the \: radius}}$

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✠ Now let's find the CSA of cylinder..!

➙ CSA = 2πrh

➙ CSA = 2(3.14)(5.8)(4)

➙ CSA = 2 × 3.14 × 5.8 × 4

➙ CSA = 6.28 × 5.8 × 4

➙ CSA = 6.28 × 23.2

➙ CSA = 140.8 cm²

${\frak{Henceforth, \: 140.8 \: cm^{2} \: is \: the \: CSA}}$

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${\large{\bold{\rm{\underline{Additional \; information}}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Volume \: of \: cylinder \: = \: \pi r^{2}h}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Surface \: area \: of \: cylinder \: = \: 2 \pi rh + 2 \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Lateral \: area \: of \: cylinder \: = \: 2 \pi rh}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Base \: area \: of \: cylinder \: = \: \pi r^{2}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Height \: of \: cylinder \: = \: \dfrac{v}{\pi r^{2}}}}}$

$\; \; \; \; \; \; \;{\sf{\bold{\leadsto Radius \: of \: cylinder \: = \:\sqrt \dfrac{v}{\pi h}}}}$

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