Question

how to derive the formula of the volume of the cube

Answer 1

Volume is actually equal to area of square corresponding to cube*height
If side is l than area=l²
Volume will be=l²*l=l³

Answer 2

VOLUME OF CUBE:

Area of the base horizontal cross section of the cube is a square shape plane figure.

area of this plane square = a² ( ‘a’ is its side)

Then area of the 2nd Square, placed just above it = a²

This way we continue & we go up to a height of ‘a’ unit.

=> area of ‘a' such sections= a * a² = a^3

SO, This total area will be the space occupied by the solid in the space.

=> VOLUME ( CUBE) = a^3 ●●●●●●●●●(1)

Similary we may derive the formulae of VOLUME of cuboid & pyramids …….

2● VOLUME OF CUBOID =

Area of the base rectangular section = a * b ( a,b are length & breadth)

If there are total ‘h' such horizontal cross sections.. ie height = h

So total area covered by all these sections =

= h x( ab)

=> VOLUME OF CUBOID = a * b * h ●●●●●●(2)