What will happen to the volume of a cube, if its edge. halved             (ii)  trebled?

Explanation

(i)Halved
Initial measure of edge of the cube is `a`.
Initial volume`=a^3`
Now, if the edge is halved:
New measure of edge of the cube`=1/2a`
New volume of the cube`=(1/2a)^3=1/8a^3`
New volume of the cube`=1/8times`Initial volume of the cube
Hence, the volume of the cube will be `1/8` times the initial volume of the cube.

(ii) Trebled
Initial measure of edge of the cube is `a`.
Initial volume`=a^3`
Now, if the edge is trebled:
New measure of edge of the cube`=3a`
New volume of the cube`=(3a)^3=27a^3`
New volume of the cube`=27times`Initial volume of the cube
Hence, the volume of the cube will be `27` times the initial volume of the cube.