Compare Circle Circumference vs Square Perimeter: 10cm Shapes

To solve this problem, we'll compare the circumference of a circle with a given diameter to the perimeter of a square with a given side length.

• Step 1: Calculate the circumference of the circle.
• Step 2: Calculate the perimeter of the square.
• Step 3: Compare the two results.

Let's work through these steps:

Step 1:
The formula for the circumference of a circle is $C = \pi \times d$. Given that the diameter $d = 10$ cm, we substitute to find the circumference:

$C = \pi \times 10 \approx 3.14159 \times 10 = 31.4159$ cm.

Step 2:
The formula for the perimeter of a square is $P = 4 \times \text{side length}$. With a side length of 10 cm, we compute the perimeter:

$P = 4 \times 10 = 40$ cm.

Step 3:
Now, compare the results:

- Circumference of the circle: 31.4159 cm
- Perimeter of the square: 40 cm

Since 40 cm (square) is much larger than 31.4159 cm (circle), we conclude that the square has a larger perimeter than the circle has circumference.

Therefore, the correct answer is the square.