Question

the area of the curved surface of a cylinder is 4400 cm square and the circumference of it's base is 110cm find: 1) the height of the cylinder and 2)volume of the cylinder​

Answer 1

Curved Surface Area of cylinder is 4400 cm².

Circumference of base of the cylinder is 110 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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$\star\;{\boxed{\sf{\purple{Circumference = 2 \pi r}}}}$

$:\implies\sf 2 \times \dfrac{22}{7} \times r = 110$

$:\implies\sf \dfrac{44}{7} \times r = 110$

$:\implies\sf r = 110 \times \dfrac{7}{44}$

$:\implies{\boxed{\frak{\pink{r = 17.5\;cm}}}}\;\bigstar$

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

$:\implies\sf 2 \times \dfrac{22}{7} \times 17.5 \times h = 4400$

$:\implies\sf \dfrac{770}{7} \times h = 4400$

$:\implies\sf h = 4400 \times \dfrac{7}{770}$

$:\implies{\boxed{\frak{\pink{h = 40\;cm}}}}\;\bigstar$

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Now, Finding Volume of cylinder,

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

$:\implies\sf \dfrac{22}{7} \times 17.5 \times 17.5 \times 40$

$:\implies\sf \dfrac{269500}{7}$

$:\implies{\boxed{\frak{\pink{38500\;cm^3}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\; Height\;and\;Volume\;of\; cylinder\;is\;40\;cm\;and\;38500\;cm^3\; respectively.}}}$