Question
A right circular cylinder having total surface area of
44352 cm2 is immersed in a vessel completely filled with water. If the height of the cylinder is 25% more than its radius, what is the amount of water displaced (in cm3)?Solution
Let the radius and height of the cylinder be r and h cm respectively. ∴ h = 1.25r Total surface area of the cylinder = 44352 = 2πr(h + r) ∴ 44352 = 2πr(1.25r + r) = 2πr(2.25r) = 4.5πr2 ∴ 44352 = (9/2) × (22/7) × r2 = 44352 x 7 x 2/22 x 9 ∴ r2 = 3136 ∴ r = 56 and h = 70 Amount of water displaced = Volume of the right circular cylinder = πr2h = (22/7) × (56)2 × (70) = 689920 cm³
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