Maharashtra State BoardSSC (English Medium) 9th Standard

The Length of a Road Roller is 2.1m and Its Diameter is 1.4m. for Levelling a Ground 500 Rotations of the Road Roller Were Required. - Geometry

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Sum

The length of a road roller is 2.1m and its diameter is 1.4m. For levelling a ground 500 rotations of the road roller were required. How much area of ground was levelled by the road roller? Find the cost of levelling at the rate of Rs. 7 per sq. m.

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Solution

Radius of the road roller, r = `1.4/2` = 0.7 m
Length of the road roller, h = 2.1 m
∴ Area levelled by the road roller in one rotation = Curved surface area of the road roller
= 2πrh
= 2 x `22/7` x 0.7 x 2.1
= 9.24 m2

∴ Area of the ground levelled by the road roller = Area levelled by the road roller in 500 rotations
= 500 × Area levelled by the road roller in one rotation
= 500 × 9.24
= 4620 m2

Rate of levelling the ground = Rs 7/m2
∴ Cost of levelling the ground
= Area of the ground levelled by the road roller × Rate of levelling the ground
= 4620 × 7
= Rs 32,340

Thus, the area of ground levelled by the road roller is 4620 m2 and the cost of levelling the ground is Rs 32,340.

Concept: Surface Area of a Cuboid
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APPEARS IN

Balbharati Mathematics 2 Geometry 9th Standard Maharashtra State Board
Chapter 9 Surface Area and Volume
Problem Set 9 | Q 9 | Page 123
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