Area to volume (×
The area of a triangle is ½ the area of a rectangle.
The volume of a cone is ⅓ of the volume of a paving stone.
The area of a circle is (pi/2)/2 the area of the square.
The volume of a sphere is (pi/2)/3 the volume of a cube (diameter the length of the cube)
In both cases, to go from area to volume, there is a multiplication by ⅔.
And it also works for ellipses and ellipsoids:
Ellipse: (pi/2)/2 multiplied by the diameter a and by the diameter b
Ellipsoid: (pi/2)/3 multiplied by the diameter a multiplied by the diameter b multiplied by the diameter c (which can be equal to a or b or other)
Why we don't learn this at scool ?
it's easier to calculate with diameters than radii.
What is the point of learning it? They kind of seem random and would only confuse students! It is not going to help them learn those formulas better, it will only make the subject unnecessarily confusing.
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