Compare Circle (r=3cm) vs Rectangle (7cm×3cm): Finding Greater Perimeter

To determine which shape has the greater perimeter or circumference, we begin by calculating each as follows.

Step 1: Calculate the circumference of the circle.
The formula for the circumference $C$ of a circle is $C = 2\pi r$.
Given the radius $r = 3$ cm, we have:

$C = 2\pi \times 3 = 6\pi \, \text{cm}$

Step 2: Calculate the perimeter of the rectangle.
The formula for the perimeter $P$ of a rectangle is $P = 2(l + w)$, where $l$ is the length and $w$ is the width.
Given the dimensions $l = 7$ cm and $w = 3$ cm, we have:

$P = 2(7 + 3) = 2 \times 10 = 20 \, \text{cm}$

Step 3: Compare the circumference and the perimeter.
The calculated circumference of the circle is $6\pi \approx 18.85 \, \text{cm}$ (using $\pi \approx 3.1416$).
The perimeter of the rectangle is $20 \, \text{cm}$.

Since $20 \, \text{cm} > 6\pi \, \text{cm} \approx 18.85 \, \text{cm}$, the rectangle has a greater perimeter than the circumference of the circle.

Therefore, the shape with the greater perimeter/circumference is the rectangle.