A right circular cylinder having total surface area of 2833.6 cm^{2} 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 cm^{3})?

Let the radius and height of the cylinder be r and h cm respectively. ∴ h = 1.30r Total surface area of the cylinder = 2833.6 = 2πr(h + r) ∴ 2833.6 = 2πr(1.3r + r) = 2πr(2.3r) = 4.6πr^{2} ∴ 2833.6 = (9.2/2) × (22/7) × r^{2} = 2833.6x 7 x 2/22 x 9.2 ∴ r^{2} = 196 ∴ r = 14 and h = 18.2 Amount of water displaced = Volume of the right circular cylinder = πr^{2}h = (22/7) × (14)^{2}× (18.2) = 11211.2 cm³

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