E maths - Cylinder question

anpanman SG

Diagram 1 shows a cylindrincal tank of radius 50 cm and length 120 cm. The tank is partially filled with water and placed with its curved surface on a horizontal floor.

Diagram II shows the circular cross-section of the cylinder. O is the centre of the circle. Angle AOB = 2 radians

Find the area of the internal surface of the tank which is in contact with the water in diagram 1. Ans:14700 cm2

Can't visualise the diagram 2 really. If someone can, could you help me out with this question. Cant seem to get the answer. Thanks!

Mikethm SG

For diagram 2, imagine you are looking at the cylinder from the front or back.

The answer is correct to 3 significant figures.

In your best interest, I refrained from providing the solution.

Jt061952 SG

Arc length area (contact with water) = 2 rad x 50 x 120 = 12000 cm2

the 2 vertical ends = pi x r^2 x (2 rad / 2pi) x 2 = 5000 cm^2

Area of 2 - triangles AOB = 0.5 x 50 x 50 x sin (2 rad) x 2 = 2273 cm^2

So area in contact with water = 12000 + 5000 - 2273

= 14727 cm^2