If area is how many unit squares fit within a shape, how do we fit squares in a circle? Because squares don’t fit evenly into circles, we don’t usually get an even answer when we’re looking for the area of a circle. We also need to use \( \pi \) (pi). The following video explains how to find the area of a circle from the radius.

Video Source (06:44 mins) | Transcript

Let \( r = radius \)

\( Area = \pi r^2 \)

**Standard Mathematical Formats with Pi**

When pi is part of a solution there are two ways you can display the solution. The first way is to write the number part of the solution multiplied to pi such as \( 13\pi ft \) or \( 5.3\pi cm\). We generally write the number then pi and then the units.

The second way to show your solution is to multiply the number portion of the solution to pi and then round to an appropriate place value. (Example: \( 13\pi ft = 40.84 ft \) rounded to the nearest hundredth)

In this course, we will always multiply pi into our solution and round to an appropriate place value. Just know that the other way is commonly used, and you may see it in textbooks or other classes as a standard way to write solutions when pi is involved.

## Additional Resources

- Khan Academy: Area of a Circle (4:01 mins; Transcript)
- Khan Academy: Area of a Circle Intuition (9:25 mins; Transcript)

### Practice Problems

- A circle has a radius of 21.5. Find the area of the circle. Round to the nearest tenth. (Solution
- A button is in the shape of a circle. If the radius of the button is 7 mm, find the surface area of the top of the button. Round to the nearest hundredth. (Solution
- A helicopter landing pad has a diameter of 28 meters or a radius of 14 meters. Find the surface area of the landing pad. Round your answer to the nearest whole number. (SolutionVideo Solution
- A rock is thrown into a pond and creates circular ripples that radiate away from the center. At one point, the largest ripple has a radius of 7.25 feet. Find the surface area of the ripple. Round to the nearest tenth. (Solution
- A frisbee is a circular disk tossed back and forth between players in a game. If the radius of the frisbee is 5 inches, find the surface area of the top of the frisbee. Round to the nearest tenth. (Solution
- A cellphone tower has the ability to provide service to a circular region with a radius of 40.3 miles. Find the total surface area of the coverage zone. Round to the nearest hundredth. (Video Solution

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