Question

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? [4 MARKS]

Answer 1

Concept : 1 Mark
Solution: 3 Marks

Let the size of cube = a

Volume of cube (V)
$=a^3$

Surface area of cube(S)
$=6a^2$

Since the side doubled, let the new side be 2a.

(i) New surface area
$=6\left(\right(2a{)}^2)=24a^2=4S$
The surface area will increase by 4 times.

(ii) New volume of cube
$=(2a{)}^3=8a^3=8V$
The volume will increase by 8 times.