A theme park ride has a ride that is located in a sphere. The ride goes around the widest circle of the sphere which has a circumference of 521.24 yd. What is the surface area of the sphere? Use 3.14

The surface area of the sphere is 86525.84 square yards

Step-by-step explanation:

The widest circle of the sphere has the same radius of the sphere

Use the circumference of the circle to find its radius, then use it to find the surface area of the sphere

The formula of the circumference of the circle is C = 2π r

The formula of the surface area of the sphere is SA = 4π r²

∵ The circumference of the widest circle is 521.24 yards

∴ C = 521.24

- Equate the formula of the circumference by it

∴ 2π r = 521.24

∵ π ≈ 3.14

∴ 2 (3.14) r = 521.24

∴ 6.28 r = 521.24

- Divide both sides by 6.28

∴ r = 83 yards

Now use the formula of the surface area of the sphere to find it

∵ The radius of the sphere = the radius of the widest circle

∴ The radius of the sphere is 83 yards

∵ SA = 4π r²

- Substitute r by 83 and π by 3.14

∴ SA = 4 (3.14) (83) ²

∴ SA = 86525.84

The surface area of the sphere is 86525.84 square yards