Question

Spaceship Earth, a spherical attraction at Walt Disney World’s Epcot Center, has a diameter of 50 meters. Find the surface area of the structure. JUSTIFY

Answer 1

The surface area of the structure ≅ 7854 meter²

Explanation:

* Lets revise the surface area of the sphere

- The surface area of a sphere is the same as the lateral surface area

of a cylinder having the same radius as the sphere and a height

equal the length of the diameter of the sphere.

- The lateral surface area of the cylinder is 2πrh

- The height of the cylinder = 2r , then the surface area of the sphere is

2πr(2r) = 4πr²

* Now lets solve the problem

∵ The sphere has diameter = 50 meters

∵ The diameter is twice the radius

∴ 2r = 50 meters ⇒ divide both sides by 2

∴ r = 25 meters

∵ The surface area of the sphere = 4πr²

∴ The surface area of the sphere = 4π(25)² = 7853.98

∴ The surface area of the sphere ≅ 7854 meters²

Answer 2

≈ 7854 m²

Explanation:

The surface area (A) of a sphere is calculated as

A = 4π r² ← r is the radius

here diameter = 50, hence r = 25, so

A= 4π × 25²

= 4π × 625 = 2500π ≈ 7854 m²