Question

area and circumference of a circle

1

discuss if it is possible to form a circle with the same area and circumference. justify your answer with an example.

posts: 1 root 01/07/2026 02:52 pm

Explanation:

Step1: Recall formulas

The formula for the area of a circle is \( A=\pi r^{2} \) and the formula for the circumference is \( C = 2\pi r \), where \( r \) is the radius of the circle.

Step2: Set area equal to circumference

We set \( \pi r^{2}=2\pi r \).

Step3: Solve for r

Divide both sides of the equation \( \pi r^{2}=2\pi r \) by \( \pi r \) (assuming \( r
eq0 \)). We get \( r = 2 \). When \( r = 0 \), the "circle" is just a point, so we consider \( r=2 \).

Step4: Verify with example

For \( r = 2 \):

• Area \( A=\pi\times(2)^{2}=4\pi \)
• Circumference \( C=2\pi\times2 = 4\pi \)

So when the radius is 2, the area and circumference of the circle are both \( 4\pi \), which means it is possible to have a circle (with radius 2) where the area and circumference have the same numerical value (when we consider the formulas with \( \pi \)).

Answer:

It is possible to form a circle with the same area and circumference (in terms of their numerical values from the formulas). For a circle with radius \( r = 2 \), the area \( A=\pi r^{2}=\pi\times2^{2} = 4\pi \) and the circumference \( C = 2\pi r=2\pi\times2=4\pi \). So when the radius is 2, the area and circumference of the circle are equal (both equal to \( 4\pi \)).