Question

read the sentences below, filling in the blanks with items from this list. each item will be used once.
sector
circumference
radius
radius
radius
central point
radians
central angle
arc length
a circle is a shape defined by a set of points equidistant from a______
the distance from the center to any point on the circles edge is called the______
the total distance around the circles edge is known as the______
the length of the curved edge of a circle (arc length) can be found using the formula______multiplied by the central angle in radians.
in the arc length formula, the central angle is typically measured in______
the formula for the area of a sector is proportional to the radius and the______
a smaller central angle of a circle corresponds to a smaller______of the circles area.
when measuring the curved edge of a circle, we refer to the distance as the______
the formula for arc length is directly related to the circles______

Explanation:

• A circle is defined by points equidistant from a central point.
• The distance from center to edge is radius.
• Total distance around edge is circumference.
• Arc length formula: radius × central angle (in radians).
• Central angle in arc length formula is in radians.
• Sector area formula is proportional to radius and central angle.
• Smaller central angle → smaller sector of area.
• Curved edge distance is arc length (but here circumference is total, arc length is part. But per list, for “curved edge” in first use (total) it's circumference. Wait no: first “curved edge of a circle (arc length)” no—wait the first blank: “A circle is a shape defined by a set of points equidistant from a [central point]”. Second: “distance from center to any point… [radius]”. Third: “total distance around… [circumference]”. Fourth: “arc length… formula [radius] multiplied by…”. Fifth: “central angle… measured in [radians]”. Sixth: “area of a sector… proportional to… [central angle]”. Seventh: “smaller central angle… [sector] of area”. Eighth: “when measuring the curved edge… [circumference] (but wait no—wait the list has “arc length” but in the fourth blank, arc length formula is radius × central angle. Then eighth: if it's “curved edge” (total) it's circumference. Ninth: “arc length… related to… [radius]”.

Answer:

1. central point
2. radius
3. circumference
4. radius
5. radians
6. central angle
7. sector
8. circumference
9. radius