Curved surface area and total surface area of a right

Solution

Curved surface area of cylinder = 2 X π X radius X height Total surface area of cylinder = 2 X π X radius X (radius + height) So, (2 X π X R X H) ÷ [2 X π X R X (R + H)] = (6160/11088) Or, H ÷ (R + H) = (5/9) Or, 9H = 5R + 5H Or, 4H = 5R Or, 'H' = (5R/4) Now, 2 X (22/7) X R X (5R/4) = 6160 Or, (44/7) X R² X (5/4) = 6160 Or, R² = 784 Or, 'R' = 28 But radius cannot be negative. So, radius = 28 cm 'H' = 5 X (28/4) = 35 cm Statement I: Volume of cylinder = (22/7) X 28² X 35 = 86,240 cm³ So, statement I is false. Statement II: Required percent = [(35 - 28) ÷ 35] X 100 = 20% less So, statement II is true. Statement III: (R - H)² + RH = (28 - 35)² + 28 X 35 = 49 + 980 = 1029 (H - 3)² + 5 = (35 - 3)² + 5 = 1024 + 5 = 1029 So, statement III is true. Therefore, only statement I is false.