# circumference of a circle

**Problem 1: What is the formula to calculate the circumference of a circle, and how does it relate to the circle’s radius and diameter?**

**Solution: **The formula to calculate the circumference (C) of a circle is:

C = 2Ï€r

Where:

C is the circumference.

Ï€ is a constant its value is approximately equal to 3.14159.

r is the radius of the circle.

The circumference (C) is directly proportional to the radius (r) of the circle. It means that if you double the radius, the circumference will also double. Similarly, if you halve the radius, the circumference will halve.

The circumference is also related to the diameter (d) of the circle:

C = Ï€d

The circumference is equal to pi times the diameter.

## radius of a circle

**Problem 2: If a circle has an area of 36 square inches, what is the radius of the circle?**

**Solution:** To find the radius (r) of a circle with a given area (A), you can use the formula:

A = Ï€rÂ²

Given that the area (A) is 36 square inches, we can set up the equation as follows:

36 = Ï€rÂ²

To solve for r, divide both sides by Ï€:

rÂ² = 36 / Ï€

Now, take the square root of both sides to find r:

r = âˆš(36 / Ï€)

r â‰ˆ 3.79 inches (rounded to two decimal places)

So, the radius of the circle is approximately 3.79 inches.

## circumference of a circle

**Problem 3: Two circles have radii of 4 inches and 6 inches, respectively. What is the difference in their circumferences?**

**Solution: **To find the difference in circumferences between two circles with radii (r1 and r2), you can use the formula for circumference:

C = 2Ï€r

For the first circle with a radius of 4 inches:

C1 = 2Ï€(4) = 8Ï€ inches

For the second circle with a radius of 6 inches:

C2 = 2Ï€(6) = 12Ï€ inches

Now, find the difference in circumferences:

Difference = C2 – C1 = (12Ï€ – 8Ï€) inches = 4Ï€ inches

So, the difference in circumferences is 4Ï€ inches.

## area of a circle

**Problem 4: Given a circle with a diameter of 10 centimeters, calculate its area.**

**Solution:** To calculate the area (A) of a circle with a given diameter (d), you can use the formula:

A = Ï€rÂ²

First, find the radius (r), which is half of the diameter:

r = d / 2 = 10 cm / 2 = 5 cm

Now, plug the radius into the formula:

A = Ï€(5 cm)Â² = 25Ï€ square centimeters

So, the area of the circle is 25Ï€ square centimeters.

## radius of a circle

**Problem 5: If the circumference of a circle is 30 meters, what is its radius?**

**Solution: **To find the radius (r) of a circle with a given circumference (C), you can use the formula:

C = 2Ï€r

Given that the circumference (C) is 30 meters, we can set up the equation as follows:

30 = 2Ï€r

Now, solve for r by dividing both sides by 2Ï€:

r = 30 / (2Ï€)

r â‰ˆ 4.77 meters (rounded to two decimal places)

So, the radius of the circle is approximately 4.77 meters.