Circles

Measure the distance around a pizza and the space inside its edge.

In plain words

Friday, a pizza. The string around the edge is the circumference. The straight cut through the middle is the diameter. The radius is half of that: from the center out to the crust.

π (say “pie”) is the distance around any circle divided by its diameter. It is about 3.14. When a problem asks us to use 3.14, use that approximation. Circumference C = π × diameter d. Because a diameter is twice the radius r, we can also write C = 2 × π × r.

Area measures the flat space inside the circle, like the surface covered by cheese on a pizza. A = π × radius × radius, or A = πr². The little 2 means multiply the radius by itself. If a pizza is 10 inches across through its center, its radius is 5 inches. Use that radius, not the diameter, in the formula.

A semicircle is half a circle. A quarter circle is one fourth. A garden that is a rectangle with a half-circle stuck on is two pieces. Find each one, then add.

Examples

Try it. Then open the steps.

Example 1 of 5

The pizza string

Friday, a 10-inch pizza

A pizza has diameter 10 inches. Using π = 3.14, what is the circumference?

Measure	Value
diameter d	10 in
radius r	5 in
π	3.14

Example 2 of 5

The fountain

The park, a round fountain

A circular fountain has radius 5 meters. Radius is the distance from the center to the edge — half the diameter. Using π = 3.14, what is the area of the water?

Example 3 of 5

The soccer ball

After practice, the ball on the grass

A soccer ball has circumference 62.8 cm. Using π = 3.14, what is the diameter?

Example 4 of 5

The half window

A semicircle window over a door

A half-circle window (a semicircle) has diameter 8 feet. Diameter is the straight cut through the center. Using π = 3.14, what is the area of the glass?

Example 5 of 5

The garden bed

A rectangular bed with a curved end

A garden is a 10 ft by 6 ft rectangle with a semicircle stuck on the 6-ft side. Using π = 3.14, what is the total area?

Piece	Area
rectangle 10 × 6	60
semicircle, r = 3	?

Things to watch for

Easy to miss: Plugging the diameter into A = πr². A 10-inch pizza is not π × 10².
Do this: Radius is half the diameter. Diameter 10 means r = 5, so A = π × 5².
Easy to miss: Treating a semicircle like a full circle. Or, when you want the distance around a semicircle, forgetting to add the straight edge.
Do this: Area of a semicircle is half of πr². The curved part is half of C. Add the diameter if you need the whole outline.

24 problems · Camp, Trail, Summit

Practice Solution key