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A roller which is cylindrical in shape covers distance equal to 5 rounds per hour. The radius of wheel is 4.5 m and the height is 7 m. Find the total area covered by the roller in making 20 rounds and time taken in covering 20 rounds. (Take π = 22/7)

A roller which is cylindrical in shape covers distance equal to 5 rounds per hour. The radius of wheel is 4.5 m and the height is 7 m. Find the total area covered by the roller in making 20 rounds and time taken in covering 20 rounds. (Take π = 22/7) Correct Answer <p>3,960 m<sup>2</sup>, 4 hours</p>

Given:

Number of rounds taken by roller = 5

Radius (r) of roller = 4.5 m

Height (h) of roller = 7 m

Concepts used:

Curved surface area (CSA) of cylindrical roller = 2πrh

Calculation:

Curved surface area of roller = Area covered by roller in 1 round

CSA of roller = 2πrh

⇒ 2 × 22/7 × 4.5 × 7 m2

⇒ 198 m2

Area covered in 1 revolution = 198 m2

⇒ Area covered in 5 revolutions = 198 × 5 m2 = 990 m2

Area covered in 20 rounds = 198 × 20 m2 = 3,960 m2

Time required in covering 990 m2 = 1 hour = 60 minutes

Time required in covering 1 m2 = 60/990 minutes = 2/33 minutes

Time required on covering 20 rounds = 2/33 minutes × 3,960 m2 = 240 minutes = 4 hours

∴ Total area covered by the wheel in making 15 revolutions is 3,960 m2and time taken in covering 20 rounds are equal to 4 hours.

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