Question

read the sentences below, filling in the blanks with items from this list. each item will be used once. diameter archimedes radius circumference area diameter increases the constant π (pi) represents the ratio of the ____ of a circle to its diameter. the formula for the area of a circle is $a = πr^2$, where r stands for the __ of the circle. the distance across the circle through its center is called the __. the method of approximating the area of a circle by using polygons is inspired by __. when dividing a circle into equal triangular sectors, the combined area of the triangular sectors approaches the area of the original circle as the number of sectors __. the formula to calculate the circumference of a circle is $c = 2πr$ or $c = πd$, where d is the __. in geometry, the term used to describe the amount of space inside the boundary of a flat (2 - dimensional) shape like a circle is the ____

Explanation:

1. Pi is defined as the ratio of a circle's circumference to its diameter.
2. In the area formula $A=\pi r^2$, $r$ denotes the radius.
3. The distance across a circle through its center is the diameter.
4. Archimedes developed the polygon method for circle area approximation.
5. More equal sectors make their total area match the circle's area better, so the number increases.
6. In $C=\pi d$, $d$ represents the diameter of the circle.
7. The space inside a 2D shape like a circle is called its area.

Answer:

1. circumference
2. radius
3. diameter
4. Archimedes
5. increases
6. diameter
7. area