Final answer:
The volume of the sphere with a surface area of 25 π yd² is 62.5 π yd³.
Step-by-step explanation:
The volume of a sphere can be found using the formula V = (4/3)πr³, where r is the radius of the sphere.
Given that the surface area of the sphere is 25π yd², we can determine the radius by using the formula for the surface area of a sphere, which is A = 4πr². Rearranging this formula gives us r = sqrt(A / 4π).
Substituting the surface area into the formula, we have r = sqrt(25π / 4π) = sqrt(25/4) = 2.5 yd. Now, we can calculate the volume using the radius:
V = (4/3)π(2.5)³ = (4/3)π(15.625) = 62.5π yd³.