Geometry: Circles (Middle School)
Circumference, area, radius, diameter, and circle vocabulary
Geometry: Circles (Middle School)
Circumference, area, radius, diameter, and circle vocabulary
Geometry - Grade 6-8
- 1
A circle has a radius of 7 centimeters. What is its diameter? Explain the relationship between radius and diameter.
A radius goes halfway across the circle, and a diameter goes all the way across through the center.
The diameter is 14 centimeters. The diameter is twice the radius, so 2 × 7 = 14. - 2
A circle has a diameter of 12 inches. Find its circumference using C = pi × d.
Substitute the diameter directly into the circumference formula.
The circumference is 37.68 inches because 3.14 × 12 = 37.68. - 3
Find the area of a circle with a radius of 5 meters using A = pi × r².
Square the radius before multiplying by 3.14.
The area is 78.5 square meters because 3.14 × 5² = 3.14 × 25 = 78.5. - 4
The circumference of a circle is 31.4 centimeters. Find the diameter and the radius.
Use C = pi × d, then divide the diameter by 2.
The diameter is 10 centimeters because 31.4 ÷ 3.14 = 10. The radius is 5 centimeters because the radius is half the diameter. - 5
A bicycle wheel has a radius of 14 inches. How far does the bicycle travel in one full turn of the wheel?
The bicycle travels 87.92 inches in one full turn. One full turn equals the circumference, and 2 × 3.14 × 14 = 87.92. - 6
A circular garden has a diameter of 18 meters. What is the radius of the garden?
The radius is 9 meters because the radius is half of the diameter, and 18 ÷ 2 = 9. - 7
Circle A has a radius of 4 centimeters. Circle B has a diameter of 10 centimeters. Which circle has the greater circumference? Show your work.
Circle B has the greater circumference. Circle A has circumference 2 × 3.14 × 4 = 25.12 centimeters, and Circle B has circumference 3.14 × 10 = 31.4 centimeters. - 8
A semicircle has a radius of 6 units. Find the area of the semicircle.
Find the area of the full circle first, then divide by 2.
The area of the semicircle is 56.52 square units. A full circle has area 3.14 × 6² = 113.04 square units, and half of that is 56.52 square units. - 9
A pizza is cut into 8 equal slices from the center. What is the central angle of one slice?
All the slices are equal, so divide 360 degrees by the number of slices.
The central angle of one slice is 45 degrees. A full circle has 360 degrees, and 360 ÷ 8 = 45. - 10
A segment connects two points on a circle and passes through the center. What is this segment called, and why?
The segment is called a diameter. It is also a chord, but it is a special chord because it passes through the center of the circle. - 11
If the radius of a circle is doubled, what happens to the circumference? Explain your reasoning.
Look at how r appears in the formula C = 2 × pi × r.
The circumference doubles. Since C = 2 × pi × r, multiplying the radius by 2 also multiplies the circumference by 2. - 12
A running track is made of two straight sections that are each 50 meters long and two semicircular ends with radius 10 meters. Find the total distance around one lap.
The total distance is 162.8 meters. The two semicircular ends make one full circle, so their combined length is 2 × 3.14 × 10 = 62.8 meters. The straight sections add 50 + 50 = 100 meters, so the total is 162.8 meters. - 13
Draw a circle and label the center, one radius, one diameter, and the circumference.
Remember that the circumference is not a line inside the circle. It is the distance around the outside.
The drawing should show a circle with a center point, a radius from the center to the circle, a diameter through the center from one side to the other, and the circumference labeled as the outside edge. - 14
A sprinkler sprays water in a circular pattern with a radius of 9 meters. What area of grass does it water?
The sprinkler waters 254.34 square meters of grass because A = 3.14 × 9² = 3.14 × 81 = 254.34. - 15
A circular fountain has radius 4 meters. A circular walkway surrounds it, making the outer radius 6 meters. Find the area of the walkway only.
Find the area of the large circle and subtract the area of the smaller circle.
The area of the walkway is 62.8 square meters. The outer circle area is 3.14 × 6² = 113.04 square meters, and the fountain area is 3.14 × 4² = 50.24 square meters. The walkway area is 113.04 - 50.24 = 62.8 square meters.