Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryMedium
A designer is creating a circular logo with a diameter of 14 centimeters. What is the approximate area of the logo?
- A616 cm²
- B44 cm²
- C154 cm²
- D22 cm²
Show answer & explanationAnswer & explanation
Correct answer: C. 154 cm²
The diameter is 14 cm, so the radius (r) is half of that, which is 7 cm. The area of a circle is given by the formula A = πr². Using π ≈ 22/7 or 3.14, A = (22/7) * 7² = (22/7) * 49 = 22 * 7 = 154 cm². If using 3.14, A = 3.14 * 7² = 3.14 * 49 = 153.86 cm², which rounds to 154 cm².
Why the other options are wrong
- A. This is pi * diameter squared, an incorrect formula.
- B. This is half of the circumference (pi * d / 2), or 2 * pi * r using r=3.5.
- D. This is the circumference if r=3.5, or diameter * pi/2.
Area of a Circle
The amount of two-dimensional space enclosed within the boundary of a circle.
- Formula: A = πr², where r is the radius.
- The radius is half the diameter (r = d/2).
- Units are square units (e.g., cm², m²).
Memory trick: Pi R squared, for the area's quest, around the circle, it's the best!