Damari inflates a spherical balloon to twice its original radius. Explain to Damari why the surface area is 4 Tims as big when the radius is doubled.

The easiest way is to show him the formula for the area of a sphere:

Area = 4 π (radius)²

That’s a good thing to discuss, because it’s a good thing to remember,
and discussing it will help him remember it.

The important part to look at is the part where it says " (radius)² ".
That tells you that if you multiply the radius by (Anything), then
the area is multiplied by (Anything)².

Since he multiplied the radius by 2, the area was multiplied by (2)² = 4.

Surface area is directly proportional to the square of radius.

Thus, when radius is doubled, Surface area becomes 2² = 4 times.