Track quiz
Eight quick questions, one for each idea. Use the table if you get stuck.
| Idea | Remember |
|---|---|
| The share | Arc = θ/360 × 2πr. Sector = θ/360 × πr². One π, start to finish. |
| The rest of the circle | Major sector = πr² − minor sector. Major segment = πr² − minor segment. |
| Take the triangle away | Minor segment = sector − triangle. |
| Three triangles | 60°, 90°, 120° build from owned facts. |
| The quarter-turn segment | Its edge is one arc plus one chord, not two radii. |
| The twins | The 60° and 120° triangles both give 49√3/4, for the same radius. |
| Reading a design | Name each round piece's share of the turn. Compute it. Then add or subtract it. |
| The design decides | Add the round piece when it sticks out of the shape. Subtract it when it is cut out of the shape. |
| Walking the boundary | Count every outer edge once. A seam is not an edge. |
A sprinkler wets a third of a circular lawn, radius 7 m. π = 22/7. How many square metres are wet?
A quarter sector covers 38.5. Its triangle covers 24.5. What does the segment cover?
A chord makes 120° at the centre. The radius is 7. How long is the chord?
A quarter-circle bed has radius 7 m. Ribbon goes round its segment, between the chord and the arc. How much ribbon?
A 60° sector's triangle covers 49√3/4. What does the 120° sector's triangle cover, for the same radius?
A card is a 20-by-14 rectangle. Its rounded top is a semicircle of radius 7. What area does the card cover?
A square courtyard has side 14. Design one adds a semicircle of radius 7 outside it. Design two cuts that semicircle into it. What do the two designs cover?
The finished courtyard and bed get a brass strip round the outside. How long is the strip?
This chapter is Areas Related to Circles. It is Chapter 11 of your Mathematics book. You have now measured the pieces this chapter works with.
Next: Surface Areas and Volumes. The circles close and the solids open. The same cutting habit lifts into three dimensions.