ASVAB · Geometry

What is the area of a circle with radius 5?

Correct answer

25π

  1. A 25π
  2. B 5π
  3. C 10π
  4. D 50π

Why this is the answer

Area of a circle = πr², where r is the radius. With r = 5: A = π(5)² = 25π square units. Numerically: 25π ≈ 25 × 3.14159 ≈ 78.5 square units. Common ASVAB answer choices keep π symbolic to avoid arithmetic ambiguity. Related circle formulas: (1) Diameter = 2r (twice the radius); (2) Circumference = 2πr or πd (length around the circle); (3) Area = πr² (surface inside); (4) Arc length = (θ/360) × 2πr where θ is the central angle in degrees; (5) Sector area = (θ/360) × πr². Common error: confusing radius and diameter — read the problem carefully. The constant π ≈ 3.14 ≈ 22/7 (older approximation); for precise work, calculator π. Squaring the radius first, then multiplying by π, avoids confusion.
Source: ASVAB Math Knowledge — Circle Area

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About this topic: Geometry

Geometry on the Mathematics Knowledge section covers angles, triangles (including the Pythagorean theorem), circles, polygons, perimeter, area and volume, and basic coordinate geometry such as slope. Formulas are not provided, so they must be memorised. This is one of 19 Mathematics Knowledge questions on geometry, each with a full explanation on a single study page.

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