The area of the circle increases by a factor of 4.

If the lengths all increase by a factor of k, then the perimeter will increase by a factor of k and the area by a factor of k².

If the lengths all increase by a factor of k, then the surface area will increase by a factor of k² and the volume by a factor of k³.

The volume of Jimmy's balloon doubles, so the lengths have all increased by a factor of

3 æ Ö

2

. So the surface area has increased by a factor of

3 æ Ö

4

, so Jimmy needs

3 æ Ö

4

L

.