Question
A right circular cylinder having total surface area of
18095 cm2 is immersed in a vessel completely filled with water. If the height of the cylinder is 35% 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 = 1.35r Total surface area of the cylinder = 18095 = 2πr(h + r) ∴ 18095 = 2πr(1.35r + r) = 2πr(2.35r) = 4.7πr2 ∴ 18095 = (9.4/2) × (22/7) × r2 = 18095 x 7 x 2/22 x 9.4 ∴ r2 = 1225 ∴ r = 35 and h = 47.25 Amount of water displaced = Volume of the right circular cylinder = πr2h = (22/7) × (35)2 × (47.25) = 18193 cm³
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