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    Question

    The sum of the volumes of cylinder A and B is 68376 cm3 . The height of cylinder B is 3 cm more than the height of cylinder A. The curved surface area of cylinder A is 1584 cm2  . If the radius of cylinder A is 28 cm, then find out the diameter of cylinder B is approximately what percentage of the height of cylinder A?

    A 751.19% Correct Answer Incorrect Answer
    B 765.57% Correct Answer Incorrect Answer
    C 777.78% Correct Answer Incorrect Answer
    D 739.92% Correct Answer Incorrect Answer
    E 713.45% Correct Answer Incorrect Answer

    Solution

    Let’s assume the radius of cylinder A and B are ‘ra‘ and ‘rb‘ respectively. Let’s assume the height of cylinder A and B are ‘ha‘ and ‘hb‘ respectively. The curved surface area of cylinder A is 1584  cm2 . If the radius of cylinder A is 28 cm. curved surface area of cylinder A = 2x(22/7)xraxha 1584 = 2x22x4xha ha = 9 cm The height of cylinder B is 3 cm more than the height of cylinder A. hb = ha+3 hb = 9+3 = 12 cm The sum of the volumes of cylinder A and B is 68376  cm3 . (22/7)[(ra)2 x ha + (rb)2 x hb] = 68376 (22/7)[(28)2   x 9 + (rb)2   x 12] = 68376 [7056 + (rb)2   x 12] = 3108x7 [7056 + (rb)2   x 12] = 21756 [(rb)2   x 12] = 21756-7056 = 14700 (rb)2   = 1225 (rb) 2   = 352 rb = 35 cm Required percentage = [(2rb)/ha]x100 = [(2x35)/9]x100 = [70/9]x100 = 777.78% (approx.)

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