Math CentralQuandaries & Queries


Question from Rana, a parent:
I want to know about Circumference / Area / Volume of different shapes ie Circle , Oval ,
An Arc Trapezide etc


Volume is undefined (or zero) for these and for any 2D shapes.
Area is undefined for arcs, which are 1-dimensional.

A circle has area pi r2 and circumference 2 pi r where r is the radius (half the diameter) and pi = 3.14159265... . You can find either of area and circumference from the other.

A trapezoid's area is the product of the average of two parallel sides and the height measured perpendicularly between them. (It is possible that one side is not "perpendicularly over" the other, in which case extend them into lines and measure the perpendicular distance between those lines. Its perimeter [circumference] is the sum of its edge lengths. You cannot determine one of these from the other, but area is less than or equal to (P/4)2 with equality only for a square (which is a special type of trapezoid.)

Ovals are a very big class of shapes, for which there is no general formula for area or perimeter. [If you mean ellipses, area is pi a b where a,b are the semiaxes and there is no easy formula for perimeter.]

You can find out more about all of these using Google.



Besides using Google you can find some information by using the Quandaries and Queries page on Math Central. For example if you use the Quick Search to search for perimeter oval you can find an approximation for the perimeter of al ellipse.


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