Circles — Practice
Every circle has the same ratio of circumference to diameter. That ratio is π, and it drives both formulas.
What these questions cover
These questions use 8 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Perimeter — Distance all the way around the outside.
- Area — Space inside, measured in square units.
- Circumference — The perimeter of a circle: C = 2π r.
- π — The circumference of any circle divided by its diameter — about 3.14159.
- Radius — Centre to edge. Half the diameter.
- Diameter — All the way across through the centre. d = 2r.
- Arc — Part of the edge; a "pizza slice" bounded by two radii.
- Sector — Part of the edge; a "pizza slice" bounded by two radii.
Problem 1
Find the circumference of a circle with radius 5. Use π ≈ 3.14.
Worked answer
31.4
2 × 3.14 × 5 = 31.4
Problem 2
Find the area of a circle with radius 4. Use π ≈ 3.14.
Worked answer
50.24
42 = 16
3.14 × 16 = 50.24
Problem 3
A circle has diameter 10. Find its radius.
Worked answer
5
10 ÷ 2 = 5
Problem 4
Find the circumference of a circle with radius 7. Use π ≈ 227.
Worked answer
44
2 × 227 × 7 = 44
Problem 5
Find the area of a circle with diameter 14. Use π ≈ 227.
Worked answer
154
r = 7
227 × 49 = 154
Problem 6
A circle has circumference 62.8. Find its radius. Use π ≈ 3.14.
Worked answer
10
62.8 = 6.28r
r = 10
Problem 7
A circle has radius 6. Find its area in terms of π (enter just the number in front of π).
Worked answer
36
62 = 36
A = 36π
Problem 8
Find the area of a semicircle of radius 6, in terms of π (enter just the number in front of π).
Worked answer
18
Full circle: 36π
Half: 18π
Problem 9
A circular table has diameter 1.4 m. Find its area. Use π ≈ 227.
Worked answer
1.54
r = 0.7 m
227 × 0.49 = 1.54 m2
Problem 10
Find the arc length of a quarter circle of radius 8, in terms of π (enter just the number in front of π).
Worked answer
4
Full circumference: 16π
A quarter: 4π
Problem 11
A circle has area 49π. Find its radius.
Worked answer
7
r2 = 49
r = 7
Problem 12
Find the area of a 60° sector of a circle with radius 6, in terms of π (enter just the number in front of π).
Worked answer
6
60360 = 16
Whole circle: 36π
16 × 36π = 6π
Problem 13
A shape is a 20 m by 14 m rectangle with a semicircle of diameter 14 m on each short end. Find the perimeter. Use π ≈ 3.14.
Worked answer
83.96
The two semicircles form one circle: C = 3.14 × 14 = 43.96 m
The two long sides: 20 + 20 = 40 m
43.96 + 40 = 83.96 m
Problem 14
A circle is inscribed in a square of side 12. Find the area inside the square but outside the circle. Use π ≈ 3.14.
Worked answer
30.96
Square: 12 × 12 = 144
Circle: r = 6, so 3.14 × 36 = 113.04
144 - 113.04 = 30.96
Problem 15
Two circles share a centre, with radii 10 and 7. Find the area of the ring between them, in terms of π (enter just the number in front of π).
Worked answer
51
Outer: 100π, inner: 49π
100π - 49π = 51π
Note it is NOT π(10-7)2 = 9π.
Problem 16
Find the arc length of a 90° sector of a circle with radius 10. Use π ≈ 3.14.
Worked answer
15.7
Full circumference: 2 × 3.14 × 10 = 62.8
14 × 62.8 = 15.7