Question

a road roller takes 450 complete Revolution to move once over to level a road. find the area of the road if the diameter of a road roller is 84 cm and length is 2 metre​

Answer 1

$\underline{\underline{\sf{\maltese\:\:Question}}}$

• A Road Roller takes 450 complete Revolutions to move once over to level a Road. Find the Area of the Road if the Diameter of a road roller is 84 cm and length is 2 metre​.

$\underline{\underline{\sf{\maltese\:\:Given}}}$

• Diameter of Road Roller = 84 cm

• Length or Height of Road Roller = 2 m

• Road Roller takes 450 complete Revolutions to move once over to level a Road

$\underline{\underline{\sf{\maltese\:\:To\:Find}}}$

• Area of the Road

$\underline{\underline{\sf{\maltese\:\:Answer}}}$

• Area of Road = 23760000 cm² or 2376 m²

$\underline{\underline{\sf{\maltese\:\:Diagram}}}$

$\setlength{\unitlength}{1mm}\begin{picture}(5,5)\thicklines\multiput(-0.5,-1)(26,0){2}{\line(0,1){40}}\multiput(12.5,-1)(0,3.2){13}{\line(0,1){1.6}}\multiput(12.5,-1)(0,40){2}{\multiput(0,0)(2,0){7}{\line(1,0){1}}}\multiput(0,0)(0,40){2}{\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\multiput(18,2)(0,32){2}{\sf{42\:cm}}\put(9,17.5){\bf{2\:m}}\end{picture}$

$\underline{\underline{\sf{\maltese\:\:Calculations}}}$

Area of Road = Complete Revolutions × Area covered in one revolution

⇒ Area of Road = 450 × Area covered in one revolution

⇒ Area of Road = 450 × Lateral Surface Area of Cylinder

⇒ Area of Road = 450 × 2πrh

⇒ Area of Road = 450 × 2 × π × r × h

Since Radius = Diameter/2

⇒ Area of Road = 450 × 2 × π × (Diameter/2) × h

⇒ Area of Road = 450 × 2 × π × (84 cm/2) × h

⇒ Area of Road = 450 × 2 × π × 42 cm × h

Since π = 22/7

⇒ Area of Road = 450 × 2 × 22/7 × 41 cm × h

⇒ Area of Road = 900 × 22/7 × 42 cm × h

⇒ Area of Road = (900 × 22)/7 × 41 cm × h

⇒ Area of Road = 19800/7 × 42 cm × h

⇒ Area of Road = (19800 × 42 cm)/7  × h

⇒ Area of Road = 831600 cm/7  × h

Given h = 2 m

⇒ Area of Road = 831600 cm/7 × 2 m

We know 1 m = 100 cm

⇒ Area of Road = 831600 cm/7 × 200 cm

⇒ Area of Road = 118800 cm × 200 cm

⇒ Area of Road = 118800 × 200 cm²

⇒ Area of Road = 118800 × 200 cm²

⇒ Area of Road = 23760000 cm²

If you want to calculate in Area of Road in m², Follow the given steps :

⇒ Area of Road = 23760000 cm²

⇒ Area of Road = 23760000 × cm²

Apply rule : a² = a × a

⇒ Area of Road = 23760000 × cm × cm

We know 1 m = 100 cm ⇒ 1 cm = 1/100 cm

⇒ Area of Road = 23760000 × (1/100 m) × (1/100 m)

⇒ Area of Road = 23760000 × (1/100) × (1/100) m²

⇒ Area of Road = 23760000 × [(1 × 1)/(100 × 100)] m²

⇒ Area of Road = 23760000 × [(1 × 1)/(100 × 100)] m²

⇒ Area of Road = 23760000 × [(1 × 1)/(100 × 100)] m²

⇒ Area of Road = 23760000 × [(1)/(100 × 100)] m²

⇒ Area of Road = 23760000 × [(1)/(10000)] m²

⇒ Area of Road = 23760000 × (1/10000) m²

⇒ Area of Road = 23760000 × 1/10000 m²

⇒ Area of Road = (23760000 × 1)/10000 m²

⇒ Area of Road = 23760000/10000 m²

⇒ Area of Road = 2376/1 m²

⇒ Area of Road = 2376 m²

______________________________________________

Request :  

If there is any difficulty viewing this answer in app, Kindly see this answer at Web (https://brainly.in/) for clear steps and understanding .

See the answer at :

https://brainly.in/question/30828974

Answer 2

Question ⤵️

A road roller takes 450 complete Revolution to move once over to level a road. find the area of the road if the diameter of a road roller is 84 cm and length is 2 mmetre.

Answer ⤵️

Area of road =750× area covered in 1 revoluation

=750× lateral surface area of cylinder

=750×2πrh

Given,

$d=84cm⇒r=42cm→ \frac{42}{100} m$

h = 1m

$=750×2× \frac{22}{7} \times \frac{42}{100} \times 1$

$= \frac{1500 \times 132}{100}$

$= 1980 {m}^{2}$

Step-by-step explanation:

Hope it helps you ✌️