What is the scale factor of surface areas of the smaller sphere to the larger sphere? (2 points)
Radius of smaller sphere 250yd^3
Radius of larger sphere 686^3
To find the scale factor of the surface areas of the smaller sphere to the larger sphere, we first need to calculate the surface area of each sphere using the formula 4πr^2, where r is the radius of the sphere.
For the smaller sphere:
Radius = 250yd^3
Surface area = 4π(250)^2 = 4π(62500) = 250000π
For the larger sphere:
Radius = 686^3
Surface area = 4π(686)^2 = 4π(469396) = 1877584π
Now, we can find the scale factor by dividing the surface area of the smaller sphere by the surface area of the larger sphere:
Scale factor = Surface area of smaller sphere / Surface area of larger sphere
Scale factor = 250000π / 1877584π
Scale factor = 1.33
Therefore, the scale factor of the surface areas of the smaller sphere to the larger sphere is 1.33.