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A cylindrical road roller made of iron is 1 m long. Its internal diameter is 54 cm and the thickness of the iron sheet used in making roller is 9 cm. Find the mass of the road roller, if 1 cm3 of the iron has 7.8 gm mass.

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One of the important question for the board exam class 10 from
mensuration chapter.This question is from r d sharma class 10 maths.
chapter-16.2 question number-16 maths r d sharma,mensuration.

In this question we have to find the mass of the road roller, if 1 cm3
of the iron has 7.8 gm mass.A cylindrical road roller made of iron is
1 m long. Its internal diameter is 54 cm and the thickness of the iron
sheet used in making roller is 9 cm.

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1 Answer

  1. Given,

    Height/length of the cylindrical road roller = h = 1 m = 100 cm

    Internal Diameter of the cylindrical road roller = 54 cm

    So, the internal radius of the cylindrical road roller = 27 cm = r

    Also given, the thickness of the road roller (T) = 9 cm

    Let us assume that the outer radii of the cylindrical road roller be R.

    T = R – r

    9 = R – 27

    R = 27 + 9

    R = 36 cm

    Now,

    The volume of the iron sheet (V) = π × (R2 − r2) × h

    V = π × (362 − 272) × 100

    V = 1780.38 cm3

    Hence, the volume of the iron sheet = 1780.38 cm3

    It’s given that, mass of 1 cm3 of the iron sheet = 7.8 gm

    So, the mass of 1780.38 cm3 of the iron sheet = 1388696.4gm = 1388.7 kg

    Therefore, the mass of the road roller is 1388.7 kg

     

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