I see that this particular question provides a formula for volume of a sphere.
But generaly speaking, are we suppose to know such fomulas by heart?
No! But, you should know the formula of calculating area of common shapes like square, circle, triangle, rectangle etc.
Using this knowledge, you can calculate the area of 3D figures where one of these shapes is the base and the height is perpendicular to base.
Volume for such figures = Area of Base x Height
e.g. A cylinder - Circular base and height perpendicular to base
Volume of cylinder = Area of base x Height = π.r^2 x h
Volume of a rectangular solid = lb x h
You may also wish to remember that volume of a pyramid/cone kind of 3D figures is 1/3 x Area of Base x Height
e.g. Volume of cone = 1/3 x π.r^2 x h
Volume of pyramid with rectangular base of sides l and b = 1/3 x lb x h
Thanks. One more related question (though, not geometry, but number properties):
I know the formula for sum of consequtive intergers: sum=(average)x(number of terms).
I can remeber it becuase it is easy and makes sense.
Much harder formular is for sum of squares of consequtive integeres: I do not really understand how it works:
(sum of squares)=n(n+1)(2n+1)/6
Have you ever had a need to use this formula on GMAT?