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The radius of a road roller is 1 m , and its length is 21/22 m. When it is rolled on the ground, it takes 600 rolls to level the entire groun(d) Howev
Question

The radius of a road roller is 1 m , and its length is 21/22 m. When it is rolled on the ground, it takes 600 rolls to level the entire groun(d) However, it was found that on 10% of the ground, the roller rolled twice. What is the total area (in sq.m) of the ground? (Use π=22/7, and round off your answer to two decimal places)

A.

3287.43

B.

3272.73

C.

3200.75

D.

3460.25

Correct option is B

Given
Radius (r) = 1 m
Length (h) = 2122\frac{21}{22}​ m
Total rolls = 600
10% of ground was rolled twice
Formula Used
Curved Surface Area of cylinder = 2 × π × r × h
Solution
Area covered in one roll = 2×227×1×2122=62 × \frac{22}{7} × 1 × \frac{21}{22} = 6​ sq.m
Total area rolled in 600 rolls = 600 × 6 = 3600 sq.m
Let the actual area of the ground be A.
Area rolled once = 90% of A = 0.9A
Area rolled twice = 10% of A = 0.1A
Total effective area rolled = (0.9A × 1) + (0.1A × 2) = 1.1A
1.1A = 3600
A =36001.1=36000113272.73 \frac{3600}{1.1} = \frac{36000}{11} ≈ 3272.73​ sq.m
Final Answer
So the correct answer is (b)

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