Compare Perimeter: Circle (r=3cm) vs Square (side=7cm)

To solve the problem of determining which shape has a larger perimeter or circumference, let's apply the necessary formulas:

The given information is as follows:

• Radius of the circle: $r = 3 \, \text{cm}$
• Side length of the square: $s = 7 \, \text{cm}$

Step 1: Calculate the circumference of the circle

The formula for the circumference of a circle is $C = 2 \pi r$. Thus, substituting the given radius, we get:

$C = 2 \pi (3) = 6 \pi$

Using an approximation for $\pi \approx 3.14159$, the circumference is:

$C \approx 6 \times 3.14159 \approx 18.84954 \, \text{cm}$

Step 2: Calculate the perimeter of the square

The formula for the perimeter of a square is $P = 4s$. Substituting the given side length, we find:

$P = 4 \times 7 = 28 \, \text{cm}$

Step 3: Compare the perimeter of the square and the circumference of the circle

The calculated circumference of the circle is approximately $18.85 \, \text{cm}$, and the perimeter of the square is $28 \, \text{cm}$.

Upon comparison, $28 \, \text{cm}$ (perimeter of the square) is greater than $18.85 \, \text{cm}$ (circumference of the circle).

Therefore, the shape with the larger perimeter/circumference is the square.