Question

If each edge of a cube is doubled :

1) how many times will its surface area increase ?
2) how many times will its volume increase ?

Answer 1

Let the edge of cube be a

Surface area = 6a^2

Volume = a^3

When edge is doubled,

New Edge = 2a

New Surface area = 6 (2a)^2

= 6 × 4 a^2

= 24 a^2

New Volume = ( 2a)^3 = 8a^3

Number of times surface area increased = 24a^2 / 6a ^2 = 4

Number of times Volume increased = 8a^3/a^3

= 8

Answer 2

Step-by-step explanation:

Surface area of cube=6a2

Is sides of cube is doubled 

New surface area is =6×4a2

Divide 2 by 1

=24a2surfaceareaofcube1surfaceareaofcube2=6a224a2=4times

Surface area increased four times 

Volume of cube= a3 

Volume of new cube= (2a)3

=8a3

Divide 2 by 1

volumeofcubevolumeofnewcube=a38a3

Volume increased 8 times