The ratio of the lengths of the radil of two spheres is 5 : 8 what is the ratio of the surface area of the smaller sphere to the surface area of the larger sphere

The ratio of the small sphere's area to that of the big one is 25:64

Step-by-step explanation:

The area of a sphere can be calculated using the formula:

A = 4 π r^2

Now, since their radii are if the ratio 5:8, we can say that the radius of the small sphere is 5 while that of the big sphere is 8

For the small sphere, the value of the area will be 4 * π * 5^2 = 100 π unit

For the big sphere, the value of the area will be 4 * π * 8^2 = 256 π unit

The ratio of the smaller sphere to the larger sphere is;

100 π : 256 π

Divide through by 4

25: 64