Stage 8 - Q1 - 3 marks
Find the perimeter in terms of \(\pi\).
Hint
Include the straight diameter.
Stage 8 - Q2 - 3 marks
Find the perimeter in terms of \(\pi\).
Hint
The boundary includes two radii.
Stage 8 - Q3 - 3 marks
Find the perimeter in terms of \(\pi\).
Hint
The radius may be fractional; retain \(\pi\) exactly.
Stage 8 - Q4 - 3 marks
Find the perimeter in terms of \(\pi\).
Hint
The two semicircles make one complete circle.
Stage 8 - Q5 - 3 marks
Find the perimeter in terms of \(\pi\).
Hint
Count the three-quarter arc and two radii.
Stage 8 - Q6 - 3 marks
A semicircle of radius 6 cm is attached along one 12 cm side of a 12 cm by 9 cm rectangle. Find the outside perimeter.
Hint
Trace the outside boundary without crossing the join.
Stage 8 - Q7 - 3 marks
A quarter-circle shape has perimeter \(20+5\pi\) cm. Find its radius.
Hint
Compare the straight part with the formula for two radii.
Stage 8 - Q8 - 3 marks
A stadium has straight lengths 18 cm and semicircular ends of radius 5 cm. Its radius increases by 2 cm while the straight lengths stay fixed. Find the perimeter increase.
Hint
The straight lengths cancel when subtracting the perimeters.
Stage 8 - Q9 - 4 marks
Compare a full circle and a semicircular shape with the same radius r. Which has the greater perimeter? Justify.
Hint
Include the diameter of the semicircle before comparing.
Stage 8 - Q10 - 5 marks
Challenge: a circular sheet of radius 10 cm has a quarter sector removed. Compare the new perimeter with the original and find the exact change. Explain why removing material can increase perimeter.
Hint
Subtract the removed arc but add both newly exposed radii.