Question

the diameter of a 120 cm long roller is 84 cm It takes 1000 complete revolutions in moving once over to level a playground what is the area of the playground​

Answer 1

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Solution :

➪ Length of roller = 120 cm.

➪ Diameter of roller = 84 cm.

➪ Radius of roller =

$\dfrac{(Diameter)}{2}$

(Diameter)

= 42 cm

As we know, a roller is in the shape of cylinder.

➪Perimeter of roller = Area covered by roller in 1 one revolution = 2 × π × (radius ) × length

➪Perimeter = 2×( \dfrac{22}{7}

➪Perimeter = 44 × 6 × 120

➪Perimeter = 31,680 cm²

Therefore,

➪Area covered by wheel in 1000 revolutions

= (31,680×1000) cm²

= \dfrac{31,680,000}{10000}

10000

31,680,000

Answer = 3,168m²

Hence, Area of Playground is 3,168m²

Answer 2

Explanation:

Radius of the roller = diameter ÷ 2 = 84 ÷ 2 = 42 cm

Length of the roller = 120 cm

Curved Surface Area of the Roller (Cylindrical shape) = begin mathsize 16px style 2 πrh space space equals space 2 space cross times 22 over 7 cross times 42 space cross times space 120 space equals space 31680 space cm squared end style

Therefore the area covered by the roller in one revolution = 31680 cm2

Therefore the area covered by the roller in 1000 revolutions = 31680 × 1000 = 31680000 cm2

Therefore the area of the play ground = 31680000 cm2 = 3168 m2

→ l × b = 3168

→ l × 32 = 3168

→ l = 99 m