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?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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