Question

A theme park has a ride that is located in half a sphere. The ride goes around the widest part of the sphere, which has a circumference of 514.96 yards.What is the surface area of the sphere? Use 3.14 for pi.

Answer 1

Sphere

The surface area of the sphere is 84453.44 sq yd

Explanation:

Given the ride goes around the widest circle of the sphere whose circumference is 514.96 yd.

The widest circle of the sphere is the plane contains the sphere's center

The circumference of the widest circle is
`2\pi r` where r is radius of the sphere.

The surface area of the sphere is defined as
`4\pi r^(2)` where r is radius of the sphere.

So 514.96 =
`2\pi r`

⇒514.96= 2 × 3.14 × r

⇒ r = 514.96 ÷ (2 × 3.14)

⇒ r = 514.96 ÷ 6.28

Surface Area A =
`4\pi r^(2)`

⇒ A = 4 × 3.14 × (514.96 ÷ 6.28) × (514.96÷ 6.28)

⇒ A = 84453.44 sq yd

The surface area of the sphere is 84453.44 sq yd