Digital SATMath: Geometry and TrigonometryMedium
An architect is designing a spherical dome for a planetarium with a radius of 20 meters. To cover the dome, they need to calculate its surface area. What is the surface area of the dome?
- A1600π square meters
- B800π square meters
- C400π square meters
- D3200π square meters
Show answer & explanationAnswer & explanation
Correct answer: A. 1600π square meters
The surface area (SA) of a sphere is given by the formula SA = 4πr². Given the radius (r) is 20 meters: SA = 4 * π * (20 meters)² = 4 * π * 400 square meters = 1600π square meters.
Why the other options are wrong
- B. This is 2πr², which is the surface area of a hemisphere, not a full sphere.
- C. This is πr², the area of a circle, not a sphere's surface area.
- D. This is double the correct answer, perhaps 8πr².
Surface Area of a Sphere
The total area of the outer surface of a spherical object.
- Formula: SA = 4πr² (where r is the radius)
- Units are square (e.g., square meters, square feet).
- Represents the material needed to cover the sphere.
Memory trick: Surface area is like wrapping a gift – how much paper do you need?