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

$\huge\bf\underline{Solution:-}$

Step - by - Step-Explanation :-

As they given Curved surface of a cylinder and diameter

We have to find the Height of cylinder .

They given diamter We have to convert into always radius

Converting diameter to radius

Radius = $\frac{Diameter}{2}$

Converting radius to diamter

Diameter = 2×Radius

______________________________

So, In given problem Diameter is there

Converting into radius

Radius = diameter/2

Radius = 20/2cm

Radius = 10cm.

Now finding Height of a cylinder

As they given CSA Of cylinder

We know CSA of cylinder = 2πrh

So, CSA Of cylinder is 100cm²

Plugging values

π = $\frac{22}{7}$

r = radius of cylinder

h = height of cylinder

100cm² = 2 × $\frac{22}{7}$ × 10 × h × cm

100 cm²= 2×10×h $\frac{22}{7}$

100cm² = 20cm h $\frac{22}{7}$

$\frac{100}{20}$ cm = h × $\frac{22}{7}$

5 cm = h × $\frac{22}{7}$

22h = 7 ×5cm

22h = 35cm

h = $\frac{35}{22}$cm

h = 1.59cm

h = 1.6 cm

So, height of cylinder is 1.6cm