Question

the diameter of a roller is 84cm and its length is 120 cm.. it takes 500 complete revolutions to move once over to level a playground.find the area of the playgroundin m.

Answer 1

The diameter of a roller is 84cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playgroundin in meters square.

$\huge{\underline{\tt{\purple{ Solution-}}}}$

Given : $\sf{Diameter = 84cm}$

$\sf{Radius = 42cm}$

$\sf{ height = 120cm}$

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$\huge{\underline{\sf{\blue{CSA\:of\:cylinder = 2πrh}}}}$

$\longrightarrow \sf{= 2\times\dfrac{22}{7}\times42\times120}$

$\longrightarrow \sf{=264\times120}$

$\longrightarrow \sf\green{=31680 cm}^{2}$

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${\underline{\tt{\blue{ Area\:cover\:is\:500\:revolution = 500\times31680}}}}$

${\underline{\tt{\green{=15840000 cm}}}}$

$\longrightarrow \sf{\dfrac{=15840000}{100\times100}}$

$\huge\longrightarrow \sf\orange{=1584 m}^{2}$

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Answer 2

✬ Area = 1584 m² ✬

Step-by-step explanation:

Given:

• Diameter of roller is 84 cm.
• Length or height of roller is 120 cm.
• Roller takes 500 revolutions to level a playground.

To Find:

• What is the area of the playground in metre ?

Solution: As we know that Radius = Diameter/2

➟ Radius of roller = 84/2 = 42 cm.

Area of roller = Curved Surface area of cylinder

★ CSA of Cylinder = ( 2πrh ) sq units ★

$\implies{\rm }$ CSA = 2 x 22/7 x 42 x 120 cm²

$\implies{\rm }$ 44 x 6 x 120 cm²

$\implies{\rm }$ 31680 cm²

So , The area of roller is 31680 cm².

• Area of 1 revolution = Area of roller = 31680 cm²

∴ Area of 500 revolutions = 500 x 31680 cm²

➟ Area of playground = 15840000 cm²

➟Area of playground in (m²)

$\implies{\rm }$ 15840000 x 1/100 x 1/100 m²

$\implies{\rm }$ 1584 m²

Hence,The area of playground is 1584 m²

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★ Other Formulae of Cylinder ★

➯ Volume = πr²h cubic units.

➯ Total Surface Area = 2πr ( h + r ) sq units.