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?

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.)