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How are two ways a cylinder and a sphere different?
A cylinder 3 faces compared to one and a sphere is fully round unlike a cylinder which has a flat bootom and top.
How can you prove that the volume of a sphere is equal to the volume of a cylinder provided their radii are equal and the height of the cylinder is equal to the diameter of the sphere?
I'm quite sure this is impossible to prove, because the volume of a sphere is not equal to the volume of a cylinder with the same radius and height equal to the sphere's diameter. This can be shown as: Volume of sphere = (4*pi*r3) / 3. Volume of cylinder = pi*r2*h. Here, the height, h, of the cylinder = d = 2r. So, the volume of the cylinder = pi*r2*2r = 2*pi*r3, which obviously does not equal the volume of the sphere. The volume of half a sphere (with radius r) is equal to the volume of a cylinder(whose height is equal to its radius, r) minus the volume of a cone with the same height and radius. Therefore, the volume of a sphere is just double that. If you follow the nearby link, you can see a nice demonstration of that.
What are the solids with curved serfaces?
Sphere, cylinder and cone
What does cone cylinder and a sphere have in common?
A circular cross-section.
What 3 solid figures have curved surfaces?
sphere, cylinder, cone
