Question

A theme park has a ride that is located in a sphere. The ride goes around the widest circle of the sphere which has a circumference of 502.40 yd. What is the surface area of the​ sphere? Use 3.14 for π.

Answer 1

Sphere

The surface area of the sphere is 80384 sq yd

Step-by-step explanation:

Given the ride goes around the widest circle of the sphere whose circumference is 502.40 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 502.4 = $2\pi r$

⇒502.4 = 2 × 3.14 × r

⇒ r = 502.4 ÷ (2 × 3.14)

⇒ $r = 502.4 / 6.28$

Surface Area A = $4\pi r^{2}$

⇒ A = 4 × 3.14 × (502.4 ÷ 6.28) × (502.4 ÷ 6.28)

⇒ A = 80384 sq yd

The surface area of the sphere is 80384 sq yd