Question

The surface area of a spherical balloon is 175 cm2. If the length of the radius was six times as large, what would the surface area be?

Answer 1

The surface area of a sphere is given by 4 pi r^2
if the radius was 6 times as large, you would replace the radius in the initial equation
A=4 pi (6r)^2

Answer 2

Another route to the answer is to use the theorem that if two solids are similar, the square of the scale factor of the two solids is equal to the ratio of surface areas.
All spheres are similar.
In this case, the scale factor is 1 to 6 or (1/6).
(1/6)^2 = 175/SA
1/36 = 175/SA
SA = 6300 square cm