Question

a road roller takes 100complete revolution to move once over to level a road find the area of the road if the diameter of the road roller is 140cm and lenght is 2m
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Answer 1

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Q) A road roller takes 100 complete revolution to move once over to level a road find the area of the road if the diameter of the road roller is 140 cm and length is 2 m .

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☆ Given :

• Roller takes 100 revolutions .
• Diameter (of roller) = 140 cm = 1.4 m
• Length (of roller) = 2 m

☆ To Find :

• Area of the road = ?

☆ Solution :

• Roller is cylindrical .
• The CSA of the roller is used to level .

• Radius = 1.4m/2

$\rm \: 1 \: revolution \: of \: roller = csa$

$\rm \: 100 \: revolution \: of \: roller = 100 \times csa = area \: of \: road$

$\mapsto \rm \: area \: of \: road = 100 \times csa$

$\mapsto \rm \: area \: of \: road= 100 \times 2 \pi \: rh$

$\mapsto \rm \: area \: of \: road = 200 \times \frac{22}{ \cancel7} \times \frac{ \cancel{1.4}}{ \cancel2} \times \cancel2 \: {m}^{2}$

$\mapsto \rm \: area \: of \: road = 200 \times 22 \times 0.2 \: {m}^{2}$

$\mapsto \purple{\boxed{\rm \: {area \: of \: road = 880 \: {m}^{2} }}}$

So , The area of road would be 880 m² .

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☆ Know more about Cylinder :

• Volume of Cylinder = πr²h

• TSA of Cylinder = 2πr(h+r)

• CSA of Cylinder = 2πrh

• Area of base/top = πr²

→ The unit of volume = unit³

→ The unit of surface area = unit²

Answer 2

Given :

• Diameter of the road roller = 140 cm = 1.4 m
• Radius of the road roller = 1.4/2 = 0.7 m
• Length of road roller = 2 m
• Total revolution of the road roller = 100

To find :

• Area of the road ?

Solution :

★ According to the Question:

• 1 revolution of the road roller = Curved surface area of roller

➣ 100 revolution = 100 × CSA = Area of road

Therefore,

➻ Area of road = 100 × 2 × 22/7 × 0.7 × 2

➻ Area of road = 100 × 2 × 22 × 0.1 × 2

➻ Area of road = 100 × 88 × 1/10

➻ Area of road = 10 × 88

➻ Area of road = 880 m²

∴ Hence, Area of road is 880 m².

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★ Formulas related to it :

• Area of base of cylinder = πr²

• Curved surface area of cylinder = 2πrh

• Total surface area of cylinder = 2πr(r + h)

• Volume of cylinder = πr²h