You can
put this solution on YOUR website!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
