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    Question

    A metallic cylinder of height 14 cm and radius 6 cm is

    melted and reshaped into several cuboids of height 3 cm, length 2 cm and breadth 1 cm. If the total cost of painting the curved part of the cylinder was Rs. 'P', then find the cost of painting all the cuboids. (Take π = 22/7)
    A Rs. '(P/11) ' Correct Answer Incorrect Answer
    B Rs. '(P/9) ' Correct Answer Incorrect Answer
    C Rs. '9P' Correct Answer Incorrect Answer
    D Rs. '11P' Correct Answer Incorrect Answer
    E None of these Correct Answer Incorrect Answer

    Solution

    Volume of cylinder = πr2h {Where 'r' is radius and 'h' is height} Volume of cuboid = l x b x h {Where 'I', 'b' and 'h' are; length, breadth and height of the cuboid} So, total volume of the cylinder = (22/7) x 62 x 14 = 1584 cm3 And total volume of a cuboid = 3 x 2 x 1 = 6 cm3 So, total number of cuboids made = 1584 ÷ 6 = 264 Total surface area of cuboid = 2 x (lb + bh + lb) = 2 x {(3 x 1) + (3 x 2) + (2 x 1)} = 2 x 11 = 22 cm2 So, total surface area of all cuboids = 22 x 264 = 5808 cm2 And total surface area of the cylinder = 2πrh = 2 x (22/7) x 6 x 14 = 528 cm2 We can see that total area of all the cuboids together is (5808/528) = 11 times the area of the cylinder So, cost of painting the cuboids will be 11 times the cost of painting the cylinder = Rs. '11P'

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