What volume of a drum is actually submerged in water when 1.75 feet of its diameter of 2.5 feet is above water and has a length of 7.5 feet showing work?

Answer 1

Diameter = 2.5 feet => radius = 1.25 ft.

1.75 ft is above water => centre of drum is 0.5 feet above water

=> if angle at centre is 2x then cos(x) = 0.5/1.25 = 0.4 => x = 1.1593 radians so that 2x = 2.3186 radians.

Then submerged area = 0.5*r^2*[2x - sin(2x)]

= 0.5*1.25^2*[2.3186 - sin(2.3186)] = 1.2386 sq ft.

S submerged volume = 1.2386*7.5 = 9.29 cubic feet, approx.