7 Polygons & Circles

Charlotte is designing a circular garden and needs to find the equation of the circle. What is the equation of the garden's boundary?

• (5, -4)

• radius = 9

• (4, -5)

• (-4, 5)

• (-5, 4)

Ava is designing a circular garden with a radius of 4 meters. Select the circumference and area of the garden.

• Circumference: 4π

• Circumference: 8π

• Circumference: 64π

• Circumference: 16π

• Area: 16π

Aiden is measuring a piece of string. If one segment of the string, BC, is 4 cm and another segment, CE, is 12 cm, then possible lengths for the entire string, AC, and another segment, CD, are:

• 9 and 7

• 16 and 3

• 5 and 15

• 7 and 15

Ava is designing a circular garden and places two identical benches at points A and C on the edge of the garden. The benches are positioned such that they form an angle ∠ABC at the center of the garden. What is the measure of ∠ABC?

• 94°

• 86°

• 172°

• 47°

Joseph is investigating some interesting properties of his favorite sci-fi insignia, which is shown below. Joseph decides to recreate this insignia as a drawing on a poster. He knows that the arc intercepted by ∠A and ∠C should measure 80°. What could be the measures of ∠A and ∠C?

• ∠A = 80°, ∠C = 40°

• ∠A = 40°, ∠C = 40°

• ∠A = 40°, ∠C = 80°

• ∠A = 80°, ∠C = 160°

Arjun is designing a circular track for a school project. The circumference of the track is 60 units. What is the approximate length of the section of the track between two points, A and B, if the angle at the center is 36°? Use π = 3.14.

• 2 units

• 6 units

• 10 units

• 12 units

A Ferris wheel ride at the fair is formed by a large circular frame divided by spokes that form sectors around the frame. At the endpoints of the spokes are the buckets where people sit along the circumference of the wheel for the ride. The circle below models one example of a Ferris wheel. The arc length of each sector formed by the Ferris wheel is 3.75π meters. Which of the following is NOT true?

• A. The arcs formed between the spokes measure 22.5º.

• B. The radius of the circle is 60 meters.

• C. The area of each sector is 56.25π square meters.

• D. Each bucket on the ride travels about 188.5 meters per full revolution of the wheel.

Abigail is designing a circular garden with a shaded flower bed section. The radius of the garden is 5 inches, and the angle of the shaded section is 140 degrees. Which is closest to the area of the shaded flower bed, in square inches?

• 12

• 31

• 79

• 122

Mason is designing his own dartboard. He started by cutting a piece of wood into a circle with a diameter of 14 inches. Next he divided the circle into congruent sectors of 18° each. Which is the closest to the area, in square inches, of one sector of Mason's dartboard? (Use π = 3.14.)

• 7.7

• 30.8

• 44.0

• 153.9