Question

Curved surface of area is 17600 CM square and the circumference is 220 cm find the height of a cylinder and volume of a cylinder​

Answer 1

Curved Surface Area of cylinder is 17600 cm².

Circumference of base of the cylinder is 220 cm.

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☯ Let radius and height of cylinder be r cm and h cm respectively.

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We know that,

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$\star\;{\boxed{\sf{\purple{Circumference = 2 \pi r}}}}$

$:\implies\sf 2 \times \dfrac{22}{7} \times r = 220$

$:\implies\sf \dfrac{44}{7} \times r = 220$

$:\implies\sf r = 220 \times \dfrac{7}{44}$

$:\implies{\boxed{\frak{\pink{r = 35\;cm}}}}\;\bigstar$

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$\star\;{\boxed{\sf{\purple{CSA_{\;(cylinder)} = 2 \pi rh}}}}$

$:\implies\sf 2 \times \dfrac{22}{7} \times 35 \times h = 17600$

$:\implies\sf \frac{17600 \times 7}{2 \times 22 \times 35}$

$:\implies{\boxed{\frak{\pink{h = 80\;cm}}}}\;\bigstar$

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Now, Finding Volume of cylinder,

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$\star\;{\boxed{\sf{\purple{Volume_{\;(cylinder)} = \pi r^2h}}}}$

$:\implies\sf \dfrac{22}{7} \times 35 \times 35 \times 80$

$:\implies{\boxed{\frak{\pink{30800\;cm^3}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\; Height\;and\;Volume\;of\; cylinder\;is\;80\;cm\;and\;30800\;cm^3\; respectively.}}}$

Answer 2

Step-by-step explanation:

Curved Surface Area of cylinder is 17600 cm².

Circumference of base of the cylinder is 220 cm.

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☯ Let radius and height of cylinder be r cm and h cm respectively.

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We know that,

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\begin{gathered}\star\;{\boxed{\sf{\purple{Circumference = 2 \pi r}}}}\\ \\\end{gathered}

⋆

Circumference=2πr

\begin{gathered}:\implies\sf 2 \times \dfrac{22}{7} \times r = 220\\ \\\end{gathered}

:⟹2×

7

22

×r=220

\begin{gathered}:\implies\sf \dfrac{44}{7} \times r = 220\\ \\\end{gathered}

:⟹

7

44

×r=220

\begin{gathered}:\implies\sf r = 220 \times \dfrac{7}{44}\\ \\\end{gathered}

:⟹r=220×

44

7

\begin{gathered}:\implies{\boxed{\frak{\pink{r = 35\;cm}}}}\;\bigstar\\ \\\end{gathered}

:⟹

r=35cm

★

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\begin{gathered}\star\;{\boxed{\sf{\purple{CSA_{\;(cylinder)} = 2 \pi rh}}}}\\ \\\end{gathered}

⋆

CSA

(cylinder)

=2πrh

\begin{gathered}:\implies\sf 2 \times \dfrac{22}{7} \times 35 \times h = 17600\\ \\\end{gathered}

:⟹2×

7

22

×35×h=17600

\begin{gathered}:\implies\sf \frac{17600 \times 7}{2 \times 22 \times 35} \\ \\\end{gathered}

:⟹

2×22×35

17600×7

\begin{gathered}:\implies{\boxed{\frak{\pink{h = 80\;cm}}}}\;\bigstar\\ \\\end{gathered}

:⟹

h=80cm

★

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Now, Finding Volume of cylinder,

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\begin{gathered}\star\;{\boxed{\sf{\purple{Volume_{\;(cylinder)} = \pi r^2h}}}}\\ \\\end{gathered}

⋆

Volume

(cylinder)

=πr

2

h

\begin{gathered}:\implies\sf \dfrac{22}{7} \times 35 \times 35 \times 80\\ \\\end{gathered}

:⟹

7

22

×35×35×80

\begin{gathered}:\implies{\boxed{\frak{\pink{30800\;cm^3}}}}\;\bigstar\\ \\\end{gathered}

:⟹

30800cm

3

★

\therefore\;{\underline{\sf{Hence,\; Height\;and\;Volume\;of\; cylinder\;is\;80\;cm\;and\;30800\;cm^3\; respectively.}}}∴

Hence,HeightandVolumeofcylinderis80cmand30800cm

3

respectively.