Question
A right circular cylinder having total surface area of
17710 cm2 is immersed in a vessel completely filled with water. If the height of the cylinder is 30% 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 = 1.30r Total surface area of the cylinder = 17710 = 2πr(h + r) ∴ 17710 = 2πr(1.3r + r) = 2πr(2.3r) = 4.6πr2 ∴ 17710 = (9.2/2) × (22/7) × r2 = 17710 x 7 x 2/22 x 9.2 ∴ r2 = 1225 ∴ r = 35 and h = 45.5 Amount of water displaced = Volume of the right circular cylinder = πr2h = (22/7) × (35)2 × (45.5) = 175175 cm³
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