Stage 9 - Q1 - 3 marks
Find the shaded area. Give 2 d.p. where needed.
Hint
Identify the area of each component and whether it is added or removed.
Stage 9 - Q2 - 3 marks
Find the shaded area. Give 2 d.p. where needed.
Hint
Identify the area of each component and whether it is added or removed.
Stage 9 - Q3 - 3 marks
Find the shaded area. Give 2 d.p. where needed.
Hint
Identify the area of each component and whether it is added or removed.
Stage 9 - Q4 - 3 marks
Find the shaded area. Give 2 d.p. where needed.
Hint
Identify the area of each component and whether it is added or removed.
Stage 9 - Q5 - 3 marks
A 18 cm by 11 cm rectangle has a circular hole of radius 5 cm. Find the remaining area to 2 d.p.
Hint
The hole is removed, not added.
Stage 9 - Q6 - 4 marks
A wall is a 10 m by 10 m rectangle topped by a semicircle. Painting costs USD 4 per square metre. Find the cost to the nearest cent.
Hint
The semicircle diameter equals the rectangle width.
Stage 9 - Q7 - 3 marks
A roof shape is a rectangle of width 36 cm and height 13 cm plus a semicircle. A pupil uses the total height in the rectangle area. Explain the error.
Hint
Split the shape along the diameter of the semicircle.
Stage 9 - Q8 - 3 marks
A shape has rectangular area 96 square cm and a semicircle of diameter 12 cm. Find its exact total area.
Hint
The diameter must be halved before squaring.
Stage 9 - Q9 - 4 marks
A circle of radius 7 cm contains an unshaded right triangle with perpendicular sides 5 cm and 6 cm. Find the exact shaded area.
Hint
The triangle’s sloping side is not its perpendicular height.
Stage 9 - Q10 - 5 marks
Challenge: A rectangular panel topped by a semicircle has width 12 cm and area \((84+18\pi)\) square cm. Find its overall height and outer perimeter.
Hint
Work backwards from area, then trace only the outside boundary.