Question

4. The diameter of a roller is 84 cm 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?​

Answer 1

Answer:

1584m

2

Radius of the roller (r)=

2

84

cm=42cm

length of the roller (h)=120cm

∴ Area of the playground levelled in taking 1 complete revolution 2πrh

=2×227×42×120=31680cm

2

∴ Area of the playground

=31680×500=15840000cm

2

100×100

15840000

m

2

=1584m

2

Answer 2

Given :

• Diameter of the roller = 84cm
• Length of the roller = 120cm
• Roller takes 500 complete revolutions to move once over to level playground.

To Find :

• Area of the Playground in m²

Solution :

Steps to do :

1. Firstly we will find the radius of the roller.
2. Secondly we will find the curved surface area of the roller or area of the roller.
3. Thirdly we will find the area of the playground.
4. Fourthly we will convert the area of the playground into m².

Finding the Radius of the Roller :

• Diameter = 2 × Radius
• Radius = Diameter/2
• Radius = (84/2) cm
• Radius = 42cm

Finding Area of the Roller :

• Area of the Roller = Curved Surface Area of Roller
• Area = 2πrh
• Area = (2 × 22/7 × 42 × 120) cm²
• Area = (2 × 22 × 6 × 120) cm²
• Area = (44 × 720) cm²
• Area of Roller = 31,680 cm²

Finding Area of the Playground :

• Area of 1 revolution = Area of Roller = 31680cm²
• Area of 500 revolution = (500 × 31680) cm²
• Area of 500 revolution = 1,58,40,000 cm²

Converting the Area into m² :

• 1,58,40,000 × 1/100 × 1/100 m²
• 1,58,400 × 1/100 m²
• 1584 m²

Therefore :

• Area of the Playground is 1584m²

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