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

★Solution :

➪ Length of roller = 120 cm.

➪ Diameter of roller = 84 cm.

➪ Radius of roller = $\dfrac{(Diameter)}{2}$

= $\dfrac{84}{2}$

= 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×( $\dfrac{22}{7}$ ) × 42 × 120

➪Perimeter = 44 × 6 × 120

➪Perimeter = 31,680 cm²

Therefore,

➪Area covered by wheel in 1000 revolutions

= (31,680×1000) cm²

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

Answer = 3,168m²

Hence, Area of Playground is 3,168m²

Answer 2

Answer:

length of roller, l = 120cm

Diameter of roller, d = 84cm

so, radius of roller, r = 84/2 = 42cm

Now,

the roller is a cylinder...

Area of cylinder = 2πrl

$So, area \: of \: roller = 2 \times \frac{22}{7} \times 42 \times 120 \\ = 2 \times 22 \times 6 \times 120 \\ = 31680 \: {cm}^{2}$

Now ,

The roller takes 1000 complete revolutions in moving once over to level a playground.

So,Area of playground = area of roller× no of revolutions

= 31680 × 1000

= 31680000 cm²