Circles — Drills
Circles has 7 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills 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.
Circumference
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the circumference of a circle with radius 13. Use π ≈ 3.14.
Worked answer
81.64
2 × 3.14 × 13 = 81.64
Problem 2
Find the circumference of a circle with radius 2. Use π ≈ 3.14.
Worked answer
12.56
2 × 3.14 × 2 = 12.56
Area
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the area of a circle with radius 11. Use π ≈ 3.14.
Worked answer
379.94
112 = 121
3.14 × 121 = 379.94
Problem 2
Find the area of a circle with radius 3. Use π ≈ 3.14.
Worked answer
28.26
32 = 9
3.14 × 9 = 28.26
Parts of the whole
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A circle has radius 12. Find its diameter.
Worked answer
24
12 × 2 = 24
Problem 2
A circle has radius 16. Find its diameter.
Worked answer
32
16 × 2 = 32
Working backwards
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A circle has area 16π. Find its radius.
Worked answer
4
r2 = 16
r = 4
Problem 2
A circle has circumference 43.96. Find its radius. Use π ≈ 3.14.
Worked answer
7
43.96 ÷ 6.28 = 7
Exact
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A circle has radius 7. Find its circumference in terms of π (enter just the number in front of π).
Worked answer
14
2 × 7 = 14
C = 14π
Problem 2
A circle has radius 10. Find its circumference in terms of π (enter just the number in front of π).
Worked answer
20
2 × 10 = 20
C = 20π
Sector
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Find the area of a 180° sector of a circle with radius 4, in terms of π (enter just the number in front of π).
Worked answer
8
180360 = 12
Whole circle: 16π
12 × 16π = 8π
Problem 2
Find the area of a 90° sector of a circle with radius 8, in terms of π (enter just the number in front of π).
Worked answer
16
90360 = 14
Whole circle: 64π
14 × 64π = 16π
Composite figures
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A circle is inscribed in a square of side 18. Find the area inside the square but outside the circle. Use π ≈ 3.14.
Worked answer
69.66
Square: 18 × 18 = 324
Circle: r = 9, area = 254.34
324 - 254.34 = 69.66
Problem 2
A circle is inscribed in a square of side 14. Find the area inside the square but outside the circle. Use π ≈ 3.14.
Worked answer
42.14
Square: 14 × 14 = 196
Circle: r = 7, area = 153.86
196 - 153.86 = 42.14