Math · Plane Geometry
Area of a Circle
Hard
Math
Plane Geometry
Question
What is the area of a circle with radius 6? Express your answer in terms of π.
Answer choices
- 6π
- 12π
- 36π
- 72π
- 12π
C Correct answer: C) 36π
Set up the problem carefully before computing. Area of a circle is π times the radius squared, not π times the diameter.
Carry the arithmetic through one step at a time, double-checking signs and units. The ACT writes wrong answers to catch the most common slips, so an answer that "looks right" without verification is risky.
Plug the answer back into the original expression as a sanity check whenever the problem allows. If the substitution does not balance, you have made an arithmetic mistake earlier in the work.
The underlying rule
Area = πr² = π · 6² = 36π.
Why each wrong answer is wrong
- A) 6π: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- B) 12π: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- D) 72π: A common arithmetic or sign error leads to this value; carefully redo the calculation.
- E) 12π: A common arithmetic or sign error leads to this value; carefully redo the calculation.
Study tip
Area = πr². Circumference = 2πr. Do not confuse them — and do not square the diameter by mistake.
More Hard Plane Geometry
- Area of a TriangleA triangle has base 12 cm and height 9 cm. What is its area in square centimeters?
- Area of a CircleWhat is the area of a circle with radius 3? Express your answer in terms of π.
- Pythagorean TheoremA right triangle has legs of length 6 and 8. What is the length of its hypotenuse?
- Perimeter of a RectangleA rectangle has length 5 and width 3. What is its perimeter?
- Area of a TriangleA triangle has base 12 cm and height 7 cm. What is its area in square centimeters?