Question

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

Answer 1

⠀⠀⠀⠀⠀⠀${\huge{\underbrace{\rm{Question}}}}$

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

⠀⠀⠀⠀⠀⠀⠀${\huge{\underbrace{\rm{Answer}}}}$

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Given:

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Diameter of the cylinder is 20 cm

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Area of the curved surface is 100 m²

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To find:

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Find the volume of the cylinder.

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Solution:

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Diameter of the cylinder = 20 cm

.°. Radius of the cylinder(r) = $\sf{\dfrac{20}{2}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= $\sf{\cancel{\dfrac{20}{2}}\:cm}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀= 10 cm

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the curved surface area of the cylinder = 100 m²

Let, the height of the cylinder is h cm

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We know that,

⠀⠀⠀$\boxed{\bf{\pink{Curved\:surface\:area\:=2πrh}}}$

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Where,

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r = radius of the cylinder

h = height of the cylinder

π = 22/7

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According to the question,

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⠀⠀⠀⠀⠀$\sf{:\implies 2πrh=100}$

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⠀⠀⠀⠀⠀$\sf{:\implies 2×\dfrac{22}{7}×10×h=100}$

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⠀⠀⠀⠀⠀$\sf{:\implies h=\dfrac{100×7}{22×10×2}}$

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⠀⠀⠀⠀⠀$\sf{:\implies h=\dfrac{700}{440}}$

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⠀⠀⠀⠀⠀$\sf{:\implies h={\cancel{\dfrac{700}{440}}}}$

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⠀⠀⠀⠀⠀$\sf{:\implies h=\dfrac{35}{22}}$

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⠀⠀⠀⠀⠀$\boxed{\bf{\purple{:⟹\:h\:=1.6\:cm}}}$

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.°. height of the cylinder is 1.6 cm

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We also know that,

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⠀⠀⠀$\boxed{\bf{\pink{Volume\:of\:cylinder\:=πr^{2}h}}}$

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$\sf{:\implies Volume\:of\:the\:cylinder=πr^{2}h}$

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$\sf{:\implies Volume\:of\:the\:cylinder=\dfrac{22}{7}×(10)^{2}×1.6\:cm^{3}}$

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$\sf{:\implies Volume\:of\:the\:cylinder=\dfrac{22}{7}×10×10×1.6\:cm^{3}}$

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$\sf{:\implies Volume\:of\:the\:cylinder=502.9\:cm^{3}}$

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Therefore,

Volume of the cylinder is 502.9 cm³

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