SOLUTION: A cylindrical can has a horizontal base of radius 3.4 cm. It contains sufficient water so that when a sphere is placed inside, the water just covers the sphere. If the sphere fits

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Question 40805: A cylindrical can has a horizontal base of radius 3.4 cm. It contains sufficient water so that when a sphere is placed inside, the water just covers the sphere. If the sphere fits exactly into the can, calculate
(a) The total surface area of the can in contact with the water when the shpere is inside, giving your answer correct to the nearest cm^2 (cm square).
(b) The depth of the water in the can before the sphere was put in, giving your answer correct to the nearest mm.
Answer by astromathman(21) (Show Source):
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There is an interesting relationship between the volumes of a cylinder, a cone, and a sphere. If these three figures have the same radius and the same height (i.e. the height = 2r, equaling the diameter of the sphere), then the volumes of the cone and sphere add up to the volume of the cylinder. Sphere: , Cone: , Cylinder: . Thus the cone is 1/3 of the cylinder and the sphere is 2/3 of the cylinder.
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Now for your problem. Let's do (b) first:
b) Since the water and the sphere add up to the volume of the submerged portion of the cylinder, the water must be 1/3 of the total. Thus when the sphere is removed the water level is 1/3 the diameter of the sphere: 2.2666 cm (rounded off to the nearest mm: 2.3 cm).
a) I assume they want to know the area of the base of the can plus the lateral area up to the diameter of the sphere. That's