Question

A cylinder has a diameter of 20cm. The area of the curved surface is 100 m square . Find the height of the cylinder.​

Answer 1

Given:-

• A cylinder has a diameter of 20 cm.
• Area of the curved surface is 100 cm².

⠀

To find:-

• Height of the cylinder.

⠀

Solution:-

If the diameter of the square is 20 cm. Then,

• Radius = 10 cm

⠀

Let,

• the height of the square be h.

⠀

Here,

• Diameter (d) = 20 cm
• Radius (r) = 10 cm

⠀

★Formula used:-

${\dag}\:{\underline{\boxed{\sf{\purple{Curved\: surface\: area_{(cylinder)} = 2\pi rh}}}}}$

⠀

$\tt\longmapsto{2\pi rh = 100 cm^2}$

⠀

$\tt\longmapsto{2 \times \dfrac{22}{7} \times 10 \times h = 100}$

⠀

$\tt\longmapsto{h = \dfrac{100 \times 7}{22 \times 10 \times 2}}$

⠀

$\tt\longmapsto{h = \dfrac{700}{440}}$

⠀

$\tt\longmapsto{h = \dfrac{35}{22}}$

⠀

$\tt\longmapsto{\underline{\boxed{\orange{h = 1.6\: cm}}}}$

⠀

Hence,

• the height of the cylinder is 1.6 cm.

⠀

★More to know :-

$\sf{Area\;of\;Rectangle\;=\;Length\;\times\;Breadth}$

⠀

$\sf{Area\;of\;Square\;=\;(Side)^{2}}$

⠀

$\sf{Area\;of\;Triangle\;=\;\dfrac{1}{2}\;\times\;Base\;\times\;Height}$

⠀

$\sf{Area\;of\;Parallelogram\;=\;Base\;\times\;Height}$

⠀

$\sf{Area\;of\;Circle\;=\;\pi r^{2}}$

$\sf{Perimeter\;of\;Rectangle\;=\;2\;\times\;(Length\;+\;Breadth)}$

⠀

$\sf{Perimeter\;of\;Rectangle\;=\;4\;\times\;(Side)}$

⠀

$\sf{Perimeter\;of\;Circle\;=\;2\pi r}$

Answer 2

$Given:-</p><p></p><p>A cylinder has a diameter of 20 cm.Area of the curved surface is 100 cm².</p><p></p><p>⠀</p><p></p><p>To find:-</p><p></p><p>Height of the cylinder.</p><p></p><p>⠀</p><p></p><p>Solution:-</p><p></p><p>If the diameter of the square is 20 cm. Then,</p><p></p><p>Radius = 10 cm</p><p></p><p>⠀</p><p></p><p>Let,</p><p></p><p>the height of the square be h.</p><p></p><p>⠀</p><p></p><p>Here,</p><p></p><p>Diameter (d) = 20 cmRadius (r) = 10 cm</p><p></p><p>⠀</p><p></p><p>★Formula used:-</p><p></p><p>{\dag}\:{\underline{\boxed{\sf{\purple{Curved\: surface\: area_{(cylinder)} = 2\pi rh}}}}}†Curvedsurfacearea(cylinder)=2πrh</p><p></p><p>⠀</p><p></p><p>\tt\longmapsto{2\pi rh = 100 cm^2}⟼2πrh=100cm2</p><p></p><p>⠀</p><p></p><p>\tt\longmapsto{2 \times \dfrac{22}{7} \times 10 \times h = 100}⟼2×722×10×h=100</p><p></p><p>⠀</p><p></p><p>\tt\longmapsto{h = \dfrac{100 \times 7}{22 \times 10 \times 2}}⟼h=22×10×2100×7</p><p></p><p>⠀</p><p></p><p>\tt\longmapsto{h = \dfrac{700}{440}}⟼h=440700</p><p></p><p>⠀</p><p></p><p>\tt\longmapsto{h = \dfrac{35}{22}}⟼h=2235</p><p></p><p>⠀</p><p></p><p>\tt\longmapsto{\underline{\boxed{\orange{h = 1.6\: cm}}}}⟼h=1.6cm</p><p></p><p>⠀</p><p></p><p>Hence,</p><p></p><p>the height of the cylinder is 1.6 cm.$