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 square.​

Answer 1

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: Question :- \: \star}}}}}$

❥ 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 playground in m².

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: AnSweR :- \: \star}}}}}$

$\large{\boxed{\bold{Area\:of\: playground\:is\:=\:1584\:m²}}}$

$\Large{\underline{\underline{\bf{GiVen:-}}}}$

↠ Diameter of roller is 84 cm.

↠ Length or height of roller is 120 cm.

↠ Roller takes 500 revolutions to level a playground.

$\Large{\underline{\underline{\bf{To find :-}}}}$

❥ What is the area of the playground in m² ?

Formula required :-

$\sf\underline{\pink{\:\:\: \: \: CSA\: Of \: Cylinder \: = \: 2πrh \:\:\:}}$

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

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✒ Radius ➠ 84/2 ↠ 42 cm

$\sf\underline{\purple{\:\:\: \: \: CSA\: Of \: Cylinder \: = \: 2πrh \:\:\:}}$

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

$\➠ \sf{=264\times120}$

$\ ➠ \sf\{=31680 cm}^{2}$

So ,

✒ The area of roller is 31680 cm².

✒ Area of 1 revolution = Area of roller ↠ 31680 cm²

${\underline{\tt{{ Area\:cover\:is\:500\:revolution = 500\times31680 cm²}}}}$

$\large{\boxed{\bold{Area\:of\: playground\:=\:15840000\:cm²}}}$

✒ Area of playground in (m²).

➠ 15840000 x 1/100 x 1/100 m²

➠ 1584 m²

✒ Hence,

$\large{\boxed{\bold{Area\:of\: playground\:is\:=\:1584\:m²}}}$

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❃ Extra shots :-

✦ Formulas Related to Cylinder :-

➤ Volume of Cylinder :-

✒ V ↠ πr²h

➤ Curved surface area of cylinder :-

✒ CS ↠ 2πrh

➤ Total Surface area of cylinder :-

✒ TS ↠ 2πrh + 2πr² = 2πr (h + r)

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➤ Volume of Hollow Cylinder :-

✒ V ↠ π ( R² - r² ) h

➤ Curved Surface Area of hollow Cylinder :-

✒ CS ↠ 2π ( r + R ) h

➤ Total Surface Area of hollow Cylinder :-

✒ TS ↠ 2π ( r + R ) h + 2π ( R² - r² )

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Answer 2

☆ 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 playground in ${m}^{2}$.

☆ Solution ☆

Given

• 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.

To find

• The area of the playground in ${m}^{2}$

Step-by-Step-Explaination

Diameter of roller = 84 cm

Radius = $\frac{d}{2}$ = $\frac{84}{2}$ = 42 cm

Length of roller = 120 cm

Curved surface area of roller = 2$\pi$RH

=> 2 × $\frac{22}{7}$ × 42 × 120

=> ( 44 × 6 × 120 ) ${cm}^{2}$

=> 31680${cm}^{2}$

Distance moved by roller in 1 revolution = It's CSA = 31680${cm}^{2}$

Area of the playground = ( 500 × 31680 )${cm}^{2}$ = 15840000${cm}^{2}$

Or in meter =$\frac{15840000{cm}^{2}}{100} = 158400 {m}^{2}$