Work with circumference, area, and radius relationships, including problems expressed in terms of π.
39 original circles questions in the SAT Ranker bank, with instant scoring and an Elo-based rank once you sign up. Below are a few free samples with full explanations.
A circle in the xy-plane has its centre at (3, -2) and a radius of 5. Which equation represents this circle?
The standard form is (x - h)² + (y - k)² = r², so a centre of (3, -2) gives (x - 3)² + (y + 2)², and r = 5 gives 25 on the right. Choice with 5 on the right uses the radius instead of its square.
A circle has a radius of 9. A sector of the circle has a central angle of 40°. What is the area of the sector?
The sector is 40/360 = 1/9 of the circle, and the full area is π(9)² = 81π, so the sector has area 81π ÷ 9 = 9π. Choice 81π is the area of the whole circle.
A circle has a radius of 12. What is the length of an arc with a central angle of 60°?
The circumference is 2π(12) = 24π, and 60° is 1/6 of a full turn, so the arc is 24π ÷ 6 = 4π. Choice 24π is the whole circumference.
An inscribed angle in a circle subtends an arc measuring 80°. What is the measure of the inscribed angle?
An inscribed angle is half the measure of the arc it subtends, so the angle is 80° ÷ 2 = 40°. Choice 80° would be the central angle subtending the same arc, which is twice the inscribed angle.
An angle measures 135°. What is its measure in radians?
Multiplying by π/180 gives 135π/180, which simplifies to 3π/4 after dividing both parts by 45. As a check, 3π/4 is three quarters of the way from 0 to π, and 135° is three quarters of the way from 0° to 180°.