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Answer :
The statements that are true about circle Q are:
- The ratio of the measure of central angle PQR to the measure of the entire circle is 1/8.
- 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.
How to explain the circle?
The measure of the central angle is 45°. The measure of the entire circle is 360°. This makes the ratio of the central angle to the entire circle 45/360 = 9/72 = 1/8
To find the area of the shaded sector, this will be:
A = πr² = π(6²) = 36π
1/8(36π) = 36π/8 = 18π/4 = 9π/2 = 4.5π square units. This is not 4 square units.
The ratio of the area of the shaded sector to the area of the circle would not be the same as the ratio of the length of the arc to the area of the circle.
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