Question

What are the dimensions of:
(a) volume of a cube of edge a,
(b) volume of a sphere of radius a,
(c) the ratio of the volume of a cube of edge a to the volume of a sphere of radius a?

Answer 1

(a) Volume of a cube of edge a, $V=a\times a\times a$
i.e., [V] = L $\times$ L $\times$ L = L³

(b) Volume of a sphere of radius a, $V=\frac{4}{3}\pi (a{)}^3$
i.e., [V] = L $\times$ L $\times$ L = L³

(c) The ratio of the volume of the cube to the volume of the sphere is a dimensionless quantity.