Question

Find the curved surface area of a right circular cylinder circumference of whose base is 77 cm and the height is 6 cm

Answer 1

EXPLANATION.

Curved surface area of a right circular cylinder.

Circumference of whose base = 77 cm.

Height is = 6 cm.

As we know that,

Formula of :

Circumference = 2πr.

⇒ 2πr = 77.

⇒ 2 x 22/7 x r = 77.

⇒ 2 x 22 x r = 77 x 7.

⇒ 2 x 2 x r = 7 x 7.

⇒ 4r = 49.

⇒ r = 49/4.

As we know that,

Formula of :

Curved surface area of cylinder = 2πrh.

⇒ 2 x 22/7 x 49/4 x 6.

⇒ 22 x 7 x 3 = 462 cm².

Curved surface area of a right circular cylinder = 462 cm².

Answer 2

✴ Given :-

• ➬ Circumference of Cylinder = 77 cm
• ➬ Height = 6 cm

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✴ To Find :-

• ➬ Curved Surface Area = ?

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✴ Solution :-

❒ How to Solve :

For finding the CSA of cylinder we need radius and height so with the given information we will first find the radius and using that we will find CSA of given cylinder. Let's Solve :

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Finding the Radius :

➺ Formula Used :

$\large\blue{\bigstar}{\underline{\boxed{\red{\sf{Circumferance{\small_{(Cylinder)}} = 2π r}}}}}$

➢Here :

• ➻ Circumference = 77cm
• ➻ π = 22/7
• ➻ r = ?

➺Finding the Radius :

${:\longmapsto{\sf{Circumferance = 2 π r}}}$

${:\longmapsto{\sf{ \: \: \: \: \: 77= 2 \times \frac{22}{7} \times r}}}$

${:\longmapsto{\sf{ \: \: \: \: \: 77 \times 7= 2 \times 22 \times r}}}$

${:\longmapsto{\sf{ \: \: \: \: \: 7 \times 7= 2 \times 2 \times r}}}$

${:\longmapsto{\sf{ \: \: \: \: \: 49= 4 \times r}}}$

$\large{\red{:\longmapsto{\green{\underline{\overline{\boxed{\sf{R = \dfrac{49}{4}}}}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Finding the CSA :

➺Formula Used :

$\large\blue{\bigstar}{\underline{\boxed{\red{\sf{CSA{\small_{(Cylinder)}} = 2π rh}}}}}$

➢Here :

• ➻ CSA = Curved Surface Area = ?
• ➻ π = 22/7
• ➻ r = Radius = 49/4
• ➻ h = Height = 6cm

➺Finding the CSA :

${:\longmapsto{\sf{ CSA= 2 π rh}}}$

${:\longmapsto{\sf{ \: \: \: \: \: \: \: \: 2 \times \dfrac{22}{7} \times \dfrac{49}{4} \times 6}}}$

${:\longmapsto{\sf{ \: \: \: \: \: \: \: \: \dfrac{44}{7} \times \dfrac{294}{4} }}}$

${:\longmapsto{\sf{ \: \: \: \: \: \: \: \: \cancel\dfrac{12936}{28} }}}$

$\large{\red{:\longmapsto{\green{\underline{\overline{\boxed{\sf{CSA = 462 \: cm²}}}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━━━━━}$

❒ Therefore :

❝ Curved Surface Area of given cylinder is 462 cm². ❞

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