Question

If each edge of a cube is doubled then:1)how many times will its surface area increase. 2)how many times will its volume increase.

Answer 1

1)Let x be side of cube.
if side is doubled then it is equal to 2x
surface area with side is x then area is
6(side)^2
=6x^2
surface area when side is 2x then the area is
6(side)^2
=6(2x)^2
=24x^2
then the surface area will increase by 4 times (24x^2/6x^2)
2)let side be x
if side is doubled then it is equal to 2x
volume when side is equal to x is
(side)^3
=x^3
volume when side is equal to 2x
(side)^3
=(2x)^3
=8x^3
then the volume will increase by 8 times (8x^3/x^3)