Question

if area of cylinder is 196 metre square and the ratio of their radius and height is 1:2.find the volume of cylinder​

Answer 1

Given :

• Area of cylinder = 196 m²
• Ratio of the radius and height of the cylinder = 1 : 2

To find :

• Volume of cylinder

Knowledge required :-

→ Formula of area of cylinder :-

• Area of cylinder = 2πr(h + r)

→ Formula of volume of cylinder :-

• Volume of cylinder = πr²h

where,

Take π = 22/7

• r denotes radius
• h denotes height

Solution :

Let the radius and height of the cylinder be 1x and 2x respectively.

⠀⠀⠀⇒ Area = 2πr(h + r)

⠀⠀⠀⇒ 196 = 2 × 22/7 × 1x(2x + 1x)

⠀⠀⠀⇒ 196 = 44/7 × 1x(3x)

⠀⠀⠀⇒ 196 × 7/44 = 3x²

⠀⠀⠀⇒ 98 × 7/22 = 3x²

⠀⠀⠀⇒ 49 × 7/11 = 3x²

⠀⠀⠀⇒ 343/11 × 1/3 = x²

⠀⠀⠀⇒ √(343/33) = x

⠀⠀⠀⇒ √10.39 = x

⠀⠀⠀⇒ 3.23 = x

The value of x = 3.23

Therefore,

• Radius of the cylinder = 1x = 3.23 cm
• Height of the cylinder = 2x = 2 × 3.23 = 6.46 cm

Volume of cylinder :-

⠀⠀⠀⇒ Volume = πr²h

⠀⠀⠀⇒ Volume = 22/7 × (3.23)² × 6.46

⠀⠀⠀⇒ Volume = 22/7 × 3.23 × 3.23 × 6.46

⠀⠀⠀⇒ Volume = 211.82

Volume of cylinder = 211.82 cm³

Answer 2

Given :-

• Area of Cylinder = 196m²
• The ratio of their radius and height is 1:2.

To Find :-

• Volume of Cylinder

Solution :-

⟶ Let the Radius be x

⟶ Let the Height be 2x

According to the Situation :

⟹ Area of Cylinder = 2πr × (h + r)

⟹ 196 = 2 × 22/7 × 1x × (2x + 1x)

⟹ 196 = 2 × 22/7 × 1x × 3x

⟹ 196 / 2 = 22/7 × 1x × 3x

⟹ 98 = 22/7 × 3x²

⟹ 98 × 7 / 22 = 3x²

⟹ 686 / 22 = 3x²

⟹ 31.18 = 3x²

⟹ 31.18 / 3 = x²

⟹ 10.39 = x²

⟹ √10.39 = x

⟹ 3.23 = x

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Therefore :

• Radius = 1x = 3.23 cm
• Height = 2x = 2 × 3.23 = 6.46 cm

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Applying Volume of Cylinder :

➞ Volume of Cylinder = πr²h

➞ Volume = 22/7 × (3.23)² × 6.46

➞ Volume = 22/7 × 3.23 × 3.23 × 6.46

➞ Volume = 22/7 × 10.43 × 6.46

➞ Volume = 22/7 × 67.37

➞ Volume = 22 × 67.37 / 7

➞ Volume = 1,482.14 / 7

➞ Volume = 211.82cm³

Thus Volume of Cylinder is 211.82cm³

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