Question

Q- find the curved surface area of a right circular cylinder circumference whose base is
88 cm & the
& the height
is 5cm.​

Answer 1

Given :

• Circumference of the cylinder = 88 cm
• Height of the cylinder = 5 cm

To Find :

The curved surface area of cylinder.

Solution :

Analysis :

Here we first have to find the radius from the circumference of the cylinder. Then using the radius and height and the formula for curved surface area we can find the curved surface area of the cylinder.

Required Formula :

• Circumference = 2πr

• Curved surface area = 2πrh

where,

• r = Radius
• h = Height

Explanation :

Let the radius of the cylinder be “r” cm.

We know that if we are given the circumference of the cylinder and is asked to find the radius then our required formula is,

Circumference = 2πr

where,

• π = 22/7
• r = r cm
• Circumference = 88 cm

Using the required formula and substituting the required values,

⇒ Circumference = 2πr

⇒ 88 = 2 × 22/7 × r

⇒ 88 = 44/7 × r

⇒ 88 × 7/44 = r

⇒ 2 × 7 = r

⇒ 14 = r

∴ Radius = 14 cm.

Curved surface area :

We know that when we are given the radius and height of the cylinder and is asked to find the Curved surface area then our required formula is,

Curved surface area = 2πrh

where,

• π = 22/7
• r = 14 cm
• h = 5 cm

Using the required formula and substituting the required values,

⇒ CSA = 2πrh

⇒ CSA = 2 × 22/7 × 14 × 5

⇒ CSA = 2 × 22 × 2 × 5

⇒ CSA = 440

∴ Curved surface area = 440 cm².

Curved Surface Area of the cylinder is 440 cm².

Answer 2

Step-by-step explanation:

★ Concept :-

Here we use the concept of Curved Surface Area of Cylinder. As we see, that we are given the Circumference and the Height of the Cylinder. Then firstly, we will find out the Radius from the Circumference of the Cylinder. After that, by applying the required values in the formula of C.S.A of cylinder we will get the answer.

Let's do it !!!

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★ Formula Used :-

$\star\;\underline{\boxed{\sf{\pink{Circumference\ of\ Cylinder\ =\ \bf 2{\pi}r.}}}}$

$\star\;\underline{\boxed{\sf{\pink{C.S.A\ of\ Cylinder\ =\ \bf 2{\pi}rh.}}}}$

___________________

★ Solution :-

Given,

↬ Circumference of Cylinder = 88cm.

↬ Height of Cylinder = 5cm.

• Let the Radius of the Cylinder be "r" cm.

------------------------------------------------------------

~ For the radius of the cylinder ::

We know that,

$\sf \rightarrow {Circumference\ of\ Cylinder\ =\ \bf 2{\pi}r}$

⦾ By applying the values, we get :-

$\sf \rightarrow {Circumference\ of\ Cylinder\ =\ \bf 2{\pi}r}$

$\sf \rightarrow {88\ =\ \bf 2 \times \dfrac{22}{7} \times r}$

$\sf \rightarrow {88\ =\ \bf \dfrac{44}{7} \times r}$

$\sf \rightarrow {\cancel {88} \times \dfrac{7}{\cancel {44}}\ =\ \bf r}$

$\sf \rightarrow {2 \times 7\ =\ \bf r}$

$\sf \rightarrow {14\ =\ \bf r}$

$\bf \rightarrow {Radius,\ r\ =\ {\red {14cm.}}}$

∴ Hence, radius of cylinder = 14cm.

------------------------------------------------------------

~ For the C.S.A of cylinder ::

We know that,

$\sf \mapsto {C.S.A\ of\ Cylinder\ =\ \bf 2{\pi}rh}$

⦾ By applying the values, we get :-

$\sf \mapsto {C.S.A\ of\ Cylinder\ =\ \bf 2{\pi}rh}$

$\sf \mapsto {C.S.A\ of\ Cylinder\ =\ \bf 2 \times \dfrac{22}{\cancel {7}} \times \cancel {14} \times 5}$

$\sf \mapsto {C.S.A\ of\ Cylinder\ =\ \bf 2 \times 22 \times 2 \times 5}$

$\bf \mapsto {C.S.A\ of\ Cylinder\ =\ {\orange {440cm^2.}}}$

∴ Hence, C.S.A of cylinder = 440cm².

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$\begin{gathered} \small\boxed { \begin{array} {cc} \large\bf\dag\: {\underline{More\ to\ know}} \\ \\ \\ \bf \bigstar {C.S.A\ of\ Cylinder\ =\ 2{\pi}rh.} \\ \\ \\ \bf \bigstar {T.S.A\ of\ Cylinder\ =\ 2{\pi}r(r\ +\ h).} \\ \\ \\ \bf \bigstar {Volume\ of\ Cylinder\ =\ {\pi}r^2h.} \end{array} } \end{gathered}$