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

${\huge{\underbrace{\rm{Question:-}}}}$

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

${\huge{\underbrace{\rm{Answer:-}}}}$

${\sf{\green{\underline{\underline{Given:}}}}}$

Diameter of the cylinder is$\sf\implies{20 cm}$

Area of the curved surface is$\sf\implies{100 m²}$

${\sf{\underline{\overline{To find:-}}}}$

⠀

• Find the volume of the cylinder.

${\sf{\underline{\overline{Solution:-}}}}$

⠀⠀

Diameter of the cylinder$\sf\implies{20 cm}$

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

• the curved surface area of the cylinder

$\sf\implies{100 m²}$

$\sf\fbox{Let,}$

• the height of the cylinder is h cm

We know that,

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

Where,

r = radius of the cylinder

h = height of the cylinder

π = 22/7

According to the question,

$\sf{:\implies 2πrh=100}$

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

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

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

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

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

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

• height of the cylinder is 1.6 cm

We also know that,

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

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

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

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

Therefore,

Volume of the cylinder is 502.9 cm³

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Answer 2

Step-by-step explanation:

{\huge{\underbrace{\rm{Question:-}}}}

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:-}}}}

Answer:−

{\sf{\green{\underline{\underline{Given:}}}}}

Given:

Diameter of the cylinder is\sf\implies{20 cm}⟹20cm

Area of the curved surface is\sf\implies{100 m²}⟹100m²

{\sf{\underline{\overline{To find:-}}}}

Tofind:−

⠀

Find the volume of the cylinder.

{\sf{\underline{\overline{Solution:-}}}}

Solution:−

⠀⠀

Diameter of the cylinder\sf\implies{20 cm}⟹20cm

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

2

20

the curved surface area of the cylinder

\sf\implies{100 m²}⟹100m²

\sf\fbox{Let,}

Let,

the height of the cylinder is h cm

We know that,

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

Curvedsurfacearea=2πrh

Where,

r = radius of the cylinder

h = height of the cylinder

π = 22/7

According to the question,

\sf{:\implies 2πrh=100}:⟹2πrh=100

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

7

22

×10×h=100

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

22×10×2

100×7

\sf{:\implies h=\dfrac{700}{440}}:⟹h=

440

700

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

440

700

\sf{:\implies h=\dfrac{35}{22}}:⟹h=

22

35

\boxed{\bf{\purple{\:h\:=1.6\:cm}}}

h=1.6cm

height of the cylinder is 1.6 cm

We also know that,

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

2

h

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

7

22

×(10)

2

×1.6cm

3

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

7

22

×10×10×1.6cm

3

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

3

Therefore,

Volume of the cylinder is 502.9 cm³

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