What is the scale factor of surface areas of the smaller sphere to the larger sphere?
small- 250 yd ^3
large - 686 yd ^3
To find the scale factor of surface areas, we need to take the square root of the ratio of the volumes of the two spheres.
For the smaller sphere with a volume of 250 yd^3, the radius would be cube root of (250/((4/3) * π)) = cube root of (750/3.14) = cube root of 238.5 ≈ 6.57 yards.
For the larger sphere with a volume of 686 yd^3, the radius would be cube root of (686/((4/3) * π)) = cube root of (2058/3.14) = cube root of 654.14 ≈ 8.07 yards.
The scale factor is then 8.07 / 6.57 ≈ 1.23.
Therefore, the scale factor of surface areas of the smaller sphere to the larger sphere is approximately 1.23.