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    Question

    A cylindrical roller made of iron is 2.4 m long. Its

    internal radius is 36 cm, and the thickness of iron sheet used in making the roller is 25 cm. What is the mass (in kg) of the roller if 1 cm³ of iron has 18 g mass?
    A 10764π Correct Answer Incorrect Answer
    B 10647 π Correct Answer Incorrect Answer
    C 14067 π Correct Answer Incorrect Answer
    D 10476 π Correct Answer Incorrect Answer

    Solution

    We had given as  Length of the roller is 2.4 m. Its internal radius is 36 cm and thickness is 25 cm.1 cm3 of iron has 18g mass  If R be the external radius and r be the internal radius and h be the height of a cylinder then the volume of the material of the cylinder is π(R²  - r² )h. Then, Length of the roller (h) = 2.4 m = 240 cm The internal radius of the cylinder (r) = 36 cm The thickness of the cylinder is 25 cm External radius of the cylinder (R) = (36 + 25) = 61 cm The volume of the cylinder is π (61²  - 36² ) × 240 (3721 - 1296) x 240 2425 x 240 = 582000π cmᶾ Mass of 1 cmᶾ  iron is 18 g Mass of 582000π cm3 iron is (582000π × 18) g ⇒ 10476000π g ⇒ 10476 π kg         [∵ 1 kg = 1000 g] ∴ The mass of the roller is 10476 π kg.

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