Question

find the height of a right circular cylinder whose curved surface area is 616cm²and diameter of the base is14cm.
​

Answer 1

GivEn:

• CSA of cylinder = 616 cm²
• Diameter of cylinder = 14 cm
• Radius of cylinder = 7 cm

⠀⠀

Need to find:

• Height of cylinder?

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━

☯ Let height of cylinder be h cm.

⠀⠀

$\setlength{\unitlength}{1.5 cm} \thicklines \begin{picture}(2,0)\qbezier(0,0)(0,0)(0,2.5)\qbezier(2,0)(2,0)(2,2.5)\qbezier(0,0)(1,1)(2,0)\qbezier(0,0)( 1, - 1)(2,0) \put(2.3,1){\vector(0,1){1.5}}\put(2.3,1){\vector(0, - 1){1.2}}\put(2.3,1){ \bf h }\put(0.3,0.1){ \bf 7 cm }\put(0,0){\vector(1,0){1}}\qbezier(0,2.5)(1,1.5)(2,2.5)\qbezier(0,2.5)(1, 3.5)(2,2.5)\end{picture}$

⠀⠀

We know that,

⠀⠀

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

$:\implies\sf 2 \times \dfrac{22}{7} \times 7 \times h = 616$

$:\implies\sf 2 \times \dfrac{22}{ \cancel{7}} \times \cancel{7} \times h = 616$

$:\implies\sf 2 \times 22 \times h = 616$

$:\implies\sf h = \dfrac{616}{2 \times 22}$

$:\implies{\boxed{\frak{\pink{h = 14\;cm}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\; Height\;of\;cylinder\;is\; \bf{14\;cm}.}}}$

⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━

$\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\red{\bigstar\:More\: to \:know :}}}}}\mid}$

• CSA of cylinder = $\bf 2 \pi rh$

⠀⠀

• TSA of cylinder = $\bf 2 \pi r(h + r)$

⠀⠀

• Volume of cylinder = $\bf \pi r^2h$

Answer 2

$\bf \huge {\underline {\underline \red{AnSwEr}}}$

⠀⠀⠀⠀⠀⠀

Given

⠀⠀⠀⠀⠀⠀

• Curved Surface Area of cylinder = 616cm²

⠀⠀⠀⠀⠀⠀

• Diameter = 14cm

⠀⠀⠀⠀⠀⠀

• Radius = 7cm

⠀⠀⠀⠀⠀⠀

To Find

⠀⠀⠀⠀⠀⠀

• Height of Cylinder

⠀⠀⠀⠀⠀⠀

Solution

⠀⠀⠀⠀⠀⠀

$\bf C.S.A \: of \: cylinder = 2\pi r h$

⠀⠀⠀⠀⠀⠀

$\bf \implies {616cm}^{2} = 2 \times \frac{22}{7} \times 7 \times h$

⠀⠀⠀⠀⠀⠀

$\bf \implies 616 {cm}^{2} = 44 \times h$

⠀⠀⠀⠀⠀⠀

$\bf \implies h \times 44 = 616$

⠀⠀⠀⠀⠀⠀

$\bf \implies h = \frac{616}{44}$

⠀⠀⠀⠀⠀⠀

$\bf \implies h = 14cm$

⠀⠀⠀⠀⠀⠀

Therefore, Height of Cylinder is 14cm.