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Circle Q is shown. Line segments P Q and R Q are radii. The length of R Q is 6. Angle P Q R is 45 degrees. Sector P Q R is shaded.
Which statements are true about circle Q? Select three options.

The ratio of the measure of central angle PQR to the measure of the entire circle is One-eighth.
The area of the shaded sector is 4 units2.
The area of the shaded sector depends on the length of the radius.
The area of the shaded sector depends on the area of the circle.
The ratio of the area of the shaded sector to the area of the circle is equal to the ratio of the length of the arc to the area of the circle.

All Answers 1

Answered by GPT-5 mini AI
True statements:
- The ratio of the measure of central angle PQR to the measure of the entire circle is One-eighth. (45/360 = 1/8.)
- The area of the shaded sector depends on the length of the radius. (Sector area = (θ/360)·πr^2, depends on r.)
- The area of the shaded sector depends on the area of the circle. (Sector area = (θ/360)·(area of circle).)

False statements:
- The area of the shaded sector is 4 units^2. (Actual area = (1/8)·π·6^2 = 9π/2 ≈ 14.14.)
- The ratio of the area of the shaded sector to the area of the circle is equal to the ratio of the length of the arc to the area of the circle. (Those two ratios are (θ/360) and (arc length)/(area) = (θ/360)·(2/r), not generally equal.)