Stage 9 - Q1 - 2 marks
Find the area of the semicircle, exactly.
Hint
Area, curved arc and full perimeter are different measurements.
Stage 9 - Q2 - 2 marks
Find the arc of the semicircle, exactly.
Hint
Area, curved arc and full perimeter are different measurements.
Stage 9 - Q3 - 2 marks
Find the perimeter of the semicircle, exactly.
Hint
Area, curved arc and full perimeter are different measurements.
Stage 9 - Q4 - 2 marks
Find the area of the semicircle, exactly.
Hint
Area, curved arc and full perimeter are different measurements.
Stage 9 - Q5 - 4 marks
A semicircular window has diameter \(28\) cm. Find glass area and full frame length, exactly.
Hint
Trace the complete boundary before calculating the frame.
Stage 9 - Q6 - 4 marks
A quarter-circle garden has radius \(15\) m. Turf costs USD 4 per square metre. Find the total cost to the nearest cent.
Hint
The price applies to area, not perimeter.
Stage 9 - Q7 - 3 marks
A pupil says the perimeter of a semicircle of radius \(16\) cm is \(16\pi\) cm. Correct the answer.
Hint
The perimeter follows the entire boundary.
Stage 9 - Q8 - 4 marks
A circle of radius \(18\) cm is cut into two semicircles. Does total perimeter double?
Hint
The cut creates two new straight boundaries.
Stage 9 - Q9 - 4 marks
A semicircle has diameter \(40\) cm. Express its area using only diameter d, and evaluate it.
Hint
Both the half-circle factor and the half-diameter factor matter.
Stage 9 - Q10 - 5 marks
Challenge: A semicircle of radius 10 cm and a quarter circle have equal curved-edge lengths. Find the quarter-circle radius and compare their areas.
Hint
Equal arc lengths do not mean equal radii or areas.