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The derivation of the formula of pyramid can be gained easily based on the formula for a triangular prism. A pyramid is like two prisms joined together.
The volume of a cube is V = x3. The derivative of this is (d/dV)x = 3x2.
Volume=lbh in a cube,l=b=h therefore,volume=a^3
Derivation of x2 or 2x is 2.
If you're able to get around in Calculus, then that derivation is a nice exercise in triple integration with polar coordinates. If not, then you just have to accept the formula after others have derived it. Actually, the formula was known before calculus was invented/discovered. Archimedes used the method of exhaustion to find the formula.