Question

A: Circumference of a circle with radius 7 inches
B: Perimeter of a square with 7 inches of sides

• A. If Quantity A is more than Quantity B
• B. If Quantity A is equal to Quantity B
• C. If Quantity A is less than Quantity B
• D. If comparison can't be made from the information given

Hint:

For comparison problems involving geometric figures, always use the appropriate formulae and compare the results numerically.

Answer 1

The Correct Option is A

Step 1: Calculate the circumference of the circle (Quantity A).
The formula for the circumference of a circle is: \[ \text{Circumference} = 2 \pi r \] Given that the radius \( r = 7 \) inches, we have: \[ \text{Circumference of the circle} = 2 \pi \times 7 = 14 \pi \approx 43.98 \text{ inches}. \] Step 2: Calculate the perimeter of the square (Quantity B).
The formula for the perimeter of a square is: \[ \text{Perimeter} = 4 \times \text{side length} \] Given that the side of the square is 7 inches, we have: \[ \text{Perimeter of the square} = 4 \times 7 = 28 \text{ inches}. \] Step 3: Comparison.
From the calculations, we know: - The circumference of the circle (Quantity A) is approximately \( 43.98 \) inches. - The perimeter of the square (Quantity B) is \( 28 \) inches. Since \( 43.98> 28 \), Quantity A is more than Quantity B. Step 4: Conclusion.
Therefore, the correct answer is option (1): Quantity A is more than Quantity B.