Will it be true to say that the perimeter of a square circumscribing a circle of radius a cm is \(8a\) cm?
Step 1: The circle has radius \(a\) cm. The diameter of the circle is twice the radius:
\( \text{Diameter} = 2 \times a = 2a \; \text{cm} \)
Step 2: A square circumscribing the circle means the circle just touches the middle of all four sides of the square. Therefore, the side of the square is equal to the diameter of the circle.
So, side of square = \(2a\) cm.
Step 3: The perimeter of a square is the total length around it. Formula: \( \text{Perimeter} = 4 \times \text{side} \)
Substitute the value of side:
\( \text{Perimeter} = 4 \times 2a = 8a \; \text{cm} \)
Step 4: Therefore, the statement is correct. Final Answer: True.