I have always wondered about this question: How do you derive the volumes of shapes? Why is the volume of a square based pyramid 1/3b^2(h)?? Why is the volume of a sphere 4/3(pi)r^3? Actually, in order to prove that these are the volumes of the sphere and square based pyramid, we have to use calculus. Calculus? Yup. In order to prove that 4/3(pi)r^3 is the volume of a sphere, you have to use integrals and basic knowledge of volumes. If you do not know what integrals are, that's okay! Watch out for my future blog posts on integrals! First, you have to find the cross-sectional volume of the shape. For instance, if the shape was a sphere, you find the cross-sectional volume of the 'disc' inside the sphere. This allows you to find one portion of the volume. You then integrate the prticular volume to a certain limit (of the 3d whole shape). Good luck,
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