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Show that the volume of cylinder is equal to one third the volume of cone?
It isn't. If the cylinder and the cone have the same height and radius, the cylinder has a larger volume (twice as large). If they do not have the same height and radius you need more information to prove their relative volumes.
What geometric shape has 1 circular base?
A sphere intersected by a plane, An circular ellipsoid intersected by a plane, A cylinder, A cone, and many more shapes, some of which don't even have a name!
Why is the curved surface of cone not 2pi x r x l?
Because 2Pi x r x L is the curved surface of a cylinder. Clearly a cylinder have more surface area than a cone of same height and radius. The surface of the cone is Pi x r x S where S is the slope length, so the cylinder has approximately double the surface area (note S is longer than L).
What is the formula for cylinder and cone?
Its not clear from the question what formulas are being requested, but: Surface area of a right cone (one where a line from the tip through the center of the base is perpendicular to the base) A = πr2 + π r(r2 + h2)½ Volume of a right cone V = (1/3)πr2h Surface area of a cylinder A = 2πr2 + 2πrh Volume of a cylinder V = πr2h where π is the number pi r is the radius of the figure h is the height of the figure perpendicular to the base. The equations for a slanted cone are more complex - so ask again with that specification if that is what you are looking for.
What is the definition of an irregular volume?
An irregular volume is one that has no simple equation to describe it's shape. An example would be a cylinder with a cone on it's end. The shape can often be divided into two or more regular shapes which have known equations that describe them. In this case, a cylinder and a cone. To then find the total volume of the irregular shape, you sum the volumes of the individual regular shape volumes.
