Question

If diameter of a road roller is 0.9 and its length
is 1.4 Find the number of rotations if 1980
area is pressed by it​

Answer 1

ANSWER :

After turning 500 revolutions the area pressed by the road roller is 1980.(Ans

EXPLANATION :

• The diameter of the road roller = 0.9

=> diameter = 2 × radius

=> radius = diameter/ 2

=> radius (r) = 0.9/ 2

=> r = 9/ 20

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• Length of the roller = 1.4

=> Height of the roller (h) = 1.4

= 14/ 10

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The roller is in the shape of a cylinder.

• Curved Surface Area of a cylinder =  × π × r × h

∴ => The Curved Surface Area of the roller (CSA) = 2 × π × r × h

CSA = 2 × $\frac{22}{7}$ × $\frac{9}{20}$ × $\frac{14}{10}$

= $\frac{198}{50}$

$\boxed{\begin{minipage}{30 em}\textbf{NOTE :} \\Here, CSA of the roller is required to find the area covered by the roller in 1 revolution. \\If we unroll the cylinder we see that it forms a rectangular plate whose area is equal to the CSA of the cylinder. (kindly see the attachment) \\In 1 revolution a cylinder is unrolled once. \end{minipage}}$

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Number of revolutions required :-

∴ =>  $\frac{198}{50}$ is the area covered in = 1 revolution

=> 1 unit  area covered in = $\frac{1}{\frac{198}{50} }$ = $\frac{50}{198}$

=> 1980 area covered in = 1980 × $\frac{50}{198}$

= 10 × 50

= 500

ANSWER:-

The number of revolutions after which it presses area 1980 is 500