Math, asked by deepikajain241084, 3 months ago

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​

Answers

Answered by Sweetoldsoul
5

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

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