Question

the circumference of a right circular cylinder is 220cm if the height of the cylinder is 20 find the total surface area of the cylinder(x=22/7)

Answer 1

☯ Given,

• Circumference of a right circular cylinder is 220 cm.
• Height (h) = 20 cm

☯ To Find,

• Total surface area of right circular cylinder.

☯ Solution,

As we know that,

Circumference of a right circular cylinder = 2πr

⇒ 220 = 2 × 22/7 × r

⇒ 220 = 44/7 × r

⇒ r = 7/44 × 220

⇒ r = 7 × 5

⇒ r = 35 cm

Let, total surface area of right circular cylinder be "x".

Now, we know that,

Total surface area of right circular cylinder = 2πr(r + h)

⇒ x = 2 × 22/7 × 35 (35 + 20)

⇒ x = 44/7 × 35 (55)

⇒ x = 44 × 5 (55)

⇒ x = 220 (55)

⇒ x = 12100 cm²

☯ Hence,

Total surface area of right circular cylinder is 12100 cm².

Answer 2

Step-by-step explanation:

$\frak Given = \begin{cases} &\sf{The\ circumference\ of\ a\ right\ circular\ cylinder\ is\ 220cm.} \\ &\sf{Height\ of\ the\ cylinder\ is\ 20cm.} \end{cases}$

To find:- We have to find the total surface area of a right circular cylinder ?

☯️ To find the T.S.A of cylinder first we have to find the radius of the cylinder.

So let's do !!

__________________

$\frak{\underline{\underline{\dag As\ we\ know\ that:-}}}$

$\sf\pink{\underline{Circumference_{(right\ circular\ cylinder)}\ =\ 2πr.}}$

__________________

$\frak{\underline{\underline{\dag By\ substituting\ the\ values,\ we\ get:-}}}$

$\sf : \implies {220\ =\ 2\ ×\ \dfrac{22}{7}\ ×\ r} \\ \\ \sf : \implies {220\ =\ \dfrac{44}{7}\ ×\ r} \\ \\ \sf : \implies {r\ =\ \dfrac{7}{44×220}} \\ \\ \sf : \implies {r\ =\ 7\ ×\ 5} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf r\ =\ 35cm.}}}}\bigstar$

$\frak{\underline{\underline{\dag Here,\ we\ know\ that:-}}}$

$\sf\pink{\underline{T.S.A_{(right\ circular\ cylinder)}\ =\ 2πr(r\ +\ h).}}$

☯️ Let total surface area of the right circular cylinder be x.

$\frak{\underline{\underline{\dag By\ substituting\ the\ values,\ we\ get:-}}}$

$\sf : \implies {x\ =\ 2\ ×\ \dfrac{22}{7}\ ×\ 35(35\ +\ 20)} \\ \\ \sf : \implies {x\ =\ \dfrac{44}{7}\ ×\ 35(55)} \\ \\ \sf : \implies {x\ =\ 44\ ×\ 5(55)} \\ \\ \sf : \implies {x\ =\ 220(55)} \\ \\ \sf : \implies {\purple{\underline{\boxed{\bf x\ =\ 12,100cm².}}}}\bigstar$

Hence:-

$\sf \therefore {\underline{The\ required\ surface\ area\ of\ the\ cylinder\ is\ 12,100cm².}}$