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  • A cylindrical roller 2.5 m in length, 1.75 m in radius when rolled on a road was found to cover the area of 5500 m^{2}. How many revolutions did it make?

A cylindrical roller 2.5\; m in length, 1.75\; m in radius when rolled on a road was found to cover the area of 5500\; m^{2}. How many revolutions did it make?

 

Answers (1)

Answer : 200 revolutions

It is given that when cylindrical roller is rolled on the road its covers 5500\; m^{2} area

Now,

Area covered by cylindrical roller in one revolution = curved surface area of cylinder

And we know that,

Curved surface area of cylinder =2\pi rh         (where r is the radius and h is its height)

Given length of roller =2.5\; m                        (This will be taken as height of the roller)

Cylindrical roller's radius = 1.75 m

So, Curved surface area =2 \times 3.14 \times 1.75 \times 2.5

                                        = 6.28 \times 4.375\; m^{2}

                                        = 27.475\; m^{2}

Total Area covered in one revolution = 27.475\; m^{2}

Now total area covered = 5500\; m^{2}

So, Number of revolutions =\frac{\text {Total Area}}{\text {area covered in one revolution}}

=\frac{5500}{27.475}

=200.181\cong 200

Hence, cylindrical roller makes 200 revolutions.

 

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