Question
A right circular cylinder having total surface area of
2710.4 cm2 is immersed in a vessel completely filled with water. If the height of the cylinder is 20% 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 = 1.20r Total surface area of the cylinder = 2710.4 = 2πr(h + r) ∴ 2710.4 = 2πr(1.2r + r) = 2πr(2.2r) = 4.4πr2 ∴ 2710.4 = (8.8/2) × (22/7) × r2 = 2710.4 x 7 x 2/22 x 8.8 ∴ r2 = 196 ∴ r = 14 and h = 16.8 Amount of water displaced = Volume of the right circular cylinder = πr2h = (22/7) × (14)2 × (16.8) = 10348.8 cm³
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