Stage 9 - Q1 - 3 marks
Find the shaded ring area, exactly.
Hint
Subtract areas, not radii before squaring.
Stage 9 - Q2 - 3 marks
Find the shaded area outside the inscribed circle, exactly.
Hint
Find the square side from the radius.
Stage 9 - Q3 - 3 marks
Find the shaded ring area, exactly.
Hint
Subtract areas, not radii before squaring.
Stage 9 - Q4 - 3 marks
Find the shaded area outside the inscribed circle, exactly.
Hint
Find the square side from the radius.
Stage 9 - Q5 - 4 marks
A square has side 12 cm. Design A removes one inscribed circle. Design B removes two non-overlapping semicircles of that diameter. Compare remaining areas.
Hint
Compare the removed areas before calculating decimals.
Stage 9 - Q6 - 4 marks
A circular path has inner radius 7 m and outer radius 9 m. Surfacing costs USD 5 per square metre. Find the total cost to the nearest cent.
Hint
Path width is not the radius of the shaded region.
Stage 9 - Q7 - 3 marks
A ring has radii 33 cm and 35 cm. A pupil claims its area is \(\pi(2)^2\). Explain the error.
Hint
The difference of squares is not the square of the difference.
Stage 9 - Q8 - 4 marks
A ring has inner radius r cm and width 4 cm. Derive its area in terms of r.
Hint
The radius-squared terms cancel after expansion.
Stage 9 - Q9 - 4 marks
A square with an inscribed circle is enlarged from radius 5 cm to radius 10 cm. How does the outside-circle area change?
Hint
Both dimensions of the shaded region scale together.
Stage 9 - Q10 - 5 marks
Challenge: A circular ring is 3 cm wide and has area \(45\pi\) square cm. Find its inner and outer radii, explaining why your positive answer is unique.
Hint
The two squared terms cancel after expansion.