If each edge of a cube is doubled, (i)            how many times will its surface area increase? (ii)           how many times will its volume increase?

Explanation

(i) Let the initial edge of the cube be `a`.
Initial surface area`=6a^2`
Now, if the edge of the cube is doubled
New edge`=2a`
New surface area`=6(2a)^2=4times6a^2`
New surface area`=4times`Initial surface area.
Hence, the surface area of the cube will be increased by `4` times.

(ii) Let the initial edge of the cube be `a`.
Initial volume of the cube`=a^3`
Now, if the edge of the cube is doubled
New edge of the cube`=2a`
New volume of the cube`=(2a)^3=8a^3`
New volume of the cube`=8times`Initial volume of the cube.
Hence, the new volume of the cube will be increased by `8` times.