Exploring Circles
Estimating Areas
Applying Circumference
Applying Areas of Circles
Distinguishing Area and Circumference
100
The circle below is centered at (0, 0). What is the radius of the circle?
The radius is 3 units.
100
A circle has radius 40 cm. Which of these is closest to its area?
A. 10,053 cm2
B. 5,026 cm2
C. 251 cm2
D. 126 cm2
B. 5,026 cm2
100
Circle A has a diameter of 12 cm. Circle B has a radius of 4 cm. Which circle has a larger circumference?
Circle A
100
Which circle has an area equivalent to pi?
Circle B
100
A theater set design includes a circle with a radius of 10 feet that represents the sun. You want to know how much yellow paint is needed for the set. Should you calculate the circumference or the area of the circle?
Area
200
Here is a circle with center Z and some line segments and curves joining points on the circle. Identify an example of the circle's diameter.
Segment TW and segment UX.
200
Find the area of the polygon.
The area is 16 cm2.
200
A Ferris wheel has a diameter of 250 meters. How far does a rider travel in one complete rotation around the Ferris wheel? Use 3.14 to approximate pi.
A rider travels about 785 meters in one complete rotation.
200
Priya paints a circular clock that has a diameter of 71 inches. What is the area of the circular clock? Use 3.14 for pi and round your answer to the nearest whole number.
The area is about 3,957 in2.
200
The radius of Mars is approximately 3,390 km. The equator is the circle around Mars dividing it into the northern and southern hemispheres. (The center of Mars is also the center of the equator.) What is the length of the equator? Round your answer to the nearest whole number.
The length of the equator is about 21,289 km.
300
The circumference of Priya's truck tire is 57 inches. What is the diameter of the tire? Round your answer to the nearest whole number.
The diameter of the tire is about 18 inches.
300
What is the area of this shape?
The area is 8.5 ft2.
300
A half circle is joined to a square with side lengths of 11 units. What is the perimeter of the resulting shape? Use 3.14 to approximate pi.
The perimeter is about 50.27 units.
300
A circle with an 8-inch radius is folded in half and then folded in half again. What is the area of the resulting shape? Use 3.14 to approximate pi.
The area is about 50.24 in2.
300
The circumference of a clock is about 50 cm. Estimate the radius, diameter, and area of the clock. Use 3.14 to approximate pi and round your answers to the nearest whole number.
The diameter is approximately 16 cm.
The radius is approximately 8 cm.
The area is approximately 199 cm2.
400
Noah measured the diameter and circumference of several circular objects and recorded his measurements in the table.
One of the rows from the table contains inaccurate measurements. Which object has either an inaccurate diameter or circumference?
The diameter or circumference of the coaster is inaccurate.
400
This figure is made from part of a circle and part of a square. What is the area of this figure, to the nearest square unit?
The area is about 23 square units.
400
The diameter of a car wheel is 17 inches. If the wheel makes 35 complete rotations, how far does the car travel? Round your answer to the nearest whole number.
The car travels about 1,868 inches.
400
A dinner plate has a circumference of 82 cm. What is the area of the dinner plate? Use 3.14 to approximate pi and round your answer to the nearest whole number.
The area of the plate is about 535 cm2.
400
Circle X has an area of 150 in2. The diameter of circle Y is 4 times the diameter of circle X. Find the area of circle Y.
The area of Circle Y is 2,400 in2.
500
Which of these pairs of quantities are proportional to each other? Select all that apply.
A. Radius and diameter of a circle
B. Radius and circumference of a circle
C. Radius and area of a circle
D. Diameter and circumference of a circle
A. Radius and diameter of a circle
B. Radius and circumference of a circle
D. Diameter and circumference of a circle
500
Find the area of the shaded region. Use 3.14 to approximate pi.
The area of the shaded region is about 58.75 cm2.
500
The wheels on Elena's bike are 91 inches in circumference. How many times do the wheels rotate if Elena rides 400 yards? Round your answer to the nearest whole number.
The wheels rotate about 158 times.
500
A painter needs to paint the bottom of a circular pool. The pool has a radius of 30 feet. A store sells 5-gallon cans of paint. One gallon of paint covers 300 square feet. What is the smallest number of 5-gallon cans the painter must buy to cover the bottom of the pool?
The painter must buy a minimum of 2 cans of paint.
500
Priya and Tyler are running in a field that has two concentric circles. Priya is running on the inner circle, which has a radius of 7 feet. Tyler is running on the outer circle, which is 6 feet farther out from the center than the inner circle is. In one go-round of the field, how much farther does Tyler travel than Priya? Use 3.14 to approximate pi.
Tyler travels about 37.68 feet farther than Priya.