Why would we measure volume in cubic units?Please explain why perimeter is measured in units and area is measured in square units. Please give examples to clarify your explanation.
The perimeter is a length. Length is measured in terms of appropriate units like meters, inches, etc.
Area is a product of 2 lengths. For example the area of a rectangle is the product of the length of its sides, the area of a triangle is also the product of two lengths which in this case are the length of the base and the length of the height. As a result of this area is expressed in square units, like square meters, square inches, etc.
Volume is a product of 3 lengths. For example the volume of a cuboid with sides w, l and h is w*l*h, the volume of a sphere is (4/3)*pi*r^3, etc. As a result volume is measured in cubic units, like cubic meters, cubic inches, etc.