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    Question

    Area of a rectangle is equal to the total surface area

    of a hemisphere having volume 8192 cm┬│. Find the perimeter of the rectangle if its length is 125% more than its breath. (Take ╧А = 3)
    A 208 cm Correct Answer Incorrect Answer
    B 182 cm Correct Answer Incorrect Answer
    C 156 cm Correct Answer Incorrect Answer
    D 169 cm Correct Answer Incorrect Answer
    E 221 cm Correct Answer Incorrect Answer

    Solution

    Let, the radius of the hemisphere be тАШrтАЩ cm. So according to question: (2/3) ├Ч 3 ├Ч r3 = 8192 r3 = 4096 r = 16 So, the total surface area of the hemisphere = 3 ├Ч ╧А ├Ч 16┬▓ = 3 ├Ч 3 ├Ч 16┬▓ = 2304 cm┬▓ Let the breadth of the rectangle be тАШxтАЩ cm So the length of the rectangle = 2.25x cm According to question: x ├Ч 2.25x = 2304 x┬▓ = 1024 x = 32 So the breadth of the rectangle = 32 cm Length of the rectangle = 32 ├Ч 2.25 = 72 cm So the perimeter of the rectangle = 2 ├Ч (72 + 32) = 208 cm

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