Question

if each edge of a cube is halved:
(i) How many times will surface area decrease.
(ii) How many times will it's volume decrease.

Answer 1

if each edge is halved
i)(6a^2)/(6(a/2)^2
 = srface area will decrease by four times
ii) volume = a^3
 ratio= (a^3)/((a/2)^3
         =8/1
so the volume will decrease by 8 times

Answer 2

To solve this we should know the following formulae

Surface area of cube = 6a²
Where a is the side of the cube.
Volume of cube = a³
Where a is the side of the cube.

Now the edges are halved.
So new edges will be a/2
So, volume (new) of cube = a³/2³=a³/8

Initial volume was a³
So, the volume decreases by 8 times.

For surface area:
Please refer the attachment for the answer.
Hope this will be helping you.

WARM REGARDS
Sahil khirwal