Geometry: Circles (Middle School) Worksheet

Question 1

A circle has a radius of 7 centimeters. What is its diameter? Explain the relationship between radius and diameter.

Accepted Answer

The diameter is 14 centimeters. The diameter is twice the radius, so 2 × 7 = 14.

Question 2

A circle has a diameter of 12 inches. Find its circumference using C = pi × d.

Accepted Answer

The circumference is 37.68 inches because 3.14 × 12 = 37.68.

Question 3

Find the area of a circle with a radius of 5 meters using A = pi × r².

Accepted Answer

The area is 78.5 square meters because 3.14 × 5² = 3.14 × 25 = 78.5.

Question 4

The circumference of a circle is 31.4 centimeters. Find the diameter and the radius.

Accepted Answer

The diameter is 10 centimeters because 31.4 ÷ 3.14 = 10. The radius is 5 centimeters because the radius is half the diameter.

Question 5

A bicycle wheel has a radius of 14 inches. How far does the bicycle travel in one full turn of the wheel?

Accepted Answer

The bicycle travels 87.92 inches in one full turn. One full turn equals the circumference, and 2 × 3.14 × 14 = 87.92.

Question 6

A circular garden has a diameter of 18 meters. What is the radius of the garden?

Accepted Answer

The radius is 9 meters because the radius is half of the diameter, and 18 ÷ 2 = 9.

Question 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.

Accepted Answer

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.

Question 8

A semicircle has a radius of 6 units. Find the area of the semicircle.

Accepted Answer

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.

Question 9

A pizza is cut into 8 equal slices from the center. What is the central angle of one slice?

Accepted Answer

The central angle of one slice is 45 degrees. A full circle has 360 degrees, and 360 ÷ 8 = 45.

Question 10

A segment connects two points on a circle and passes through the center. What is this segment called, and why?

Accepted Answer

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.

Question 11

If the radius of a circle is doubled, what happens to the circumference? Explain your reasoning.

Accepted Answer

The circumference doubles. Since C = 2 × pi × r, multiplying the radius by 2 also multiplies the circumference by 2.

Question 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.

Accepted Answer

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.

Question 13

Draw a circle and label the center, one radius, one diameter, and the circumference.

Accepted Answer

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.

Question 14

A sprinkler sprays water in a circular pattern with a radius of 9 meters. What area of grass does it water?

Accepted Answer

The sprinkler waters 254.34 square meters of grass because A = 3.14 × 9² = 3.14 × 81 = 254.34.

Question 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.

Accepted Answer

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.

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Geometry: Circles (Middle School)

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