Question

A road roller takes 759 complete Revolution to move once over to level a road find the area of road if diameter of road roller is 84cm and length is 2 metre

Answer 1

Given:

• A road roller takes 759 complete revolution to move once over to level a road.
• Diameter of road roller is 84 cm.
• Length of road roller is 2 metre.

Find:-

Area of road.

Solution:-

Diameter of road roller = 84 cm

Radius of road = Half of diameter

⇒ $\sf{\dfrac{84}{2}}$

⇒ $\sf{42}$ cm

To convert cm into m. Divide with 100.

⇒ $\sf{\dfrac{42}{100}}$

⇒ $\sf{0.42}$ m

Road roller takes 759 revolutions to move once over to level a road.

So, we can say that -

Area of road = Total number of revolutions × Area covered in one revolution

⇒ 759 × surface area of cylinder

⇒ $\sf{759 \:\times\: 2 \pi rh}$

⇒ $\sf{759\:\times\:2\:\times\:\frac{22}{7}\:\times\:0.42\:\times\:2}$

⇒ $\sf{1518\:\times\:\frac{22}{7}\:\times\:0.84}$

⇒ $\sf{1275.12\:\times\:\frac{22}{7}}$

⇒ $\sf{182.16\:\times\:22}$

⇒ $\sf{4007.52}$

⇒ $\sf{4008}$ (approx.)

•°• Area of the road is 4008 m².

Answer 2

${\bold{\underline{\underline{Answer:}}}}$

SOLUTION : Diameter of road roller = 84 cm

$\implies$ Radius of the road roller = 84/2 = 42 cm

$\implies$ Lenght of the roller = 2m =200 cm

$\implies$ Now, Area of the roller = π×D

= 22/7 × 84 = 264 cm

$\implies$ Length of the road = Area of the roller × number of revolutions completed by the roller.

$\implies$ Length of the road = 264 × 759 = 200,376 cm.

$\implies$ Width of the road = length of the roller

$\therefore$ Width of the road = 200 cm

$\implies$ Thus, Area of the road = length of the road × length of the roller

$\implies$ Area of the road = 200,376 × 200 = 4,007,520 cm² = 4007.52 cm or 4,008 m²