Question

What is the area of the circle?
Statement A: The radius of the circle is equal to the side of the square of the area 256 square inches.
Statement B: The width of the rectangle is 3/4 of the radius of the circle.

• A. If statement 1 alone is sufficient to answer
• B. If statement 2 alone is sufficient to answer
• C. If both the statements are needed to answer
• D. Cannot answer from both the statement using together

Hint:

When given information about the radius of a circle, use the formula \( \text{Area} = \pi r^2 \) to find the area.

Answer 1

The Correct Option is A

Step 1: Analyze Statement A.
Statement A tells us that the radius of the circle is equal to the side of a square whose area is 256 square inches. Since the area of a square is given by \( \text{side}^2 \), we can find the side of the square: \[ \text{side} = \sqrt{256} = 16 \text{ inches}. \] Thus, the radius of the circle is 16 inches. Now we can calculate the area of the circle using the formula \( \text{Area of the circle} = \pi r^2 \): \[ \text{Area of the circle} = \pi \times 16^2 = \pi \times 256 \approx 3.1416 \times 256 \approx 804.25 \text{ square inches}. \] Step 2: Analyze Statement B.
Statement B gives us information about the width of a rectangle being 3/4 of the radius of the circle, but this information is not necessary to calculate the area of the circle, as we already have sufficient information from Statement A. Step 3: Conclusion.
Statement A alone is sufficient to calculate the area of the circle. Therefore, the correct answer is option (1): Statement 1 alone is sufficient to answer.