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 m².

Solution:

The roller is cylindrical in shape and hence it is considered as a right circular cylinder. In one revolution, the area covered will be the curved surface area of the roller.

Since it takes 500 complete revolutions to move once over to level a playground, the area of the playground will be equal to 500 times the curved surface area of the roller.

Let the radius and height of the cylinder are 'r' and 'h' respectively.

Curved Surface Area of the cylinder = 2πrh

Length of the roller, h = 120 cm

Radius of the roller, r = 84/2 cm = 42 cm

Curved Surface Area of the roller = 2πrh

= 2 × 22/7 × 42 cm × 120 cm

= 31680 cm²

Area of the playground = Area leveled by the cylinder in 500 revolutions

= 500 × 31680 cm²

= 15840000 cm²

= 15840000/10000 m²  [Since 1cm² = 1/10000 m²]

= 1584 m²

Thus, area of the playground = 1584 m².

☛ Check: NCERT Solutions Class 9 Maths Chapter 13

Video Solution:

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 m²

Class 9 Maths NCERT Solutions Chapter 13 Exercise 13.2 Question 4

Summary:

It is given that 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. We have found that the area of the playground is 1584 m².

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