What are the dimensions of:(a) volume of a cube of edge a,(b) volume o

1.	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» (a) Volume of a cube of edge a, V=a×a×a i.e., [V] = L×L×L = L³ (b) Volume of a sphere of radius a, V=4/3π(a)³ i.e., [V] = L×L ×L = L³ (c) The ratio of the volume of the cube to the volume of the sphere is a dimensionless quantity.

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»

(a) Volume of a cube of edge a,

V=a×a×a

i.e.,

[V] = L×L×L = L³

(b) Volume of a sphere of radius a,

V=4/3π(a)³

i.e., [V] = L×L ×L = L³