Question

If the area and perimeter of a circle are numerically the same, then the radius of that circle will be:

• A. \( \pi \) units
• B. 4 units
• C. 7 units
• D. 2 units

Hint:

When the area and perimeter of a circle are the same, solve the equation \( \pi r^2 = 2\pi r \) to find the radius.

Answer 1

The Correct Option is D

Step 1: Write the formulas for area and perimeter.
The area \( A \) of a circle is given by: \[ A = \pi r^2 \] The perimeter (circumference) \( C \) of a circle is given by: \[ C = 2\pi r \] We are told that the area and perimeter are numerically the same. Therefore: \[ \pi r^2 = 2\pi r \]
Step 2: Simplify the equation.
Cancel \( \pi \) from both sides: \[ r^2 = 2r \]
Step 3: Solve for \( r \).
Divide both sides by \( r \) (assuming \( r \neq 0 \)): \[ r = 2 \]
Step 4: Conclusion.
Thus, the radius of the circle is 2 units. Therefore, the correct answer is (D).