Sphere 1 has surface area a1 and volume v1 and sphere 2 has surface area a2 and volume v2. if the radius of sphere 2 is 2.71 times the radius of sphere 1, what is the ratio of the areas a2/a1?

The surface area of a sphere is given by the equation AS = 4π * r ^ 2. For this formula, r equals the radius of the sphere

We have then that

a1 = 4π * r1 ^ 2

a2 = 4π * r2 ^ 2

r2 = 2.71r1

Then, dividing the areas

a2 / a1 = (4π * (2.71r1) ^ 2) / (4π * r1 ^ 2) = (7.3441 / 1) * (r1 ^ 2 / r1 ^ 2) = 7.3441

answer

the ratio of the areas a2 / a1 is 7.3441