Stage 9 - Q1 - 2 marks
Find the radius, exactly.
Hint
Area requires a square root; circumference does not.
Stage 9 - Q2 - 2 marks
Find the diameter, exactly.
Hint
Area requires a square root; circumference does not.
Stage 9 - Q3 - 2 marks
A circle has area 254.47 square cm. Estimate its radius to 2 d.p.
Hint
Choose the inverse formula appropriate to the measurement.
Stage 9 - Q4 - 2 marks
Find the area, exactly.
Hint
The radius is the bridge between the two measurements.
Stage 9 - Q5 - 3 marks
A semicircle has area \(\frac{121}{2}\pi\) square cm. Find its diameter.
Hint
The given area is only half of the full circle.
Stage 9 - Q6 - 3 marks
A wheel of diameter 24 cm makes 70 full turns without slipping. Find the distance travelled in metres to 2 d.p.
Hint
One turn travels one circumference.
Stage 9 - Q7 - 3 marks
A pupil uses \(r=A\div\pi\) when a circle has area \(225\pi\) square cm. Explain and correct the error.
Hint
Track what the area formula squares.
Stage 9 - Q8 - 3 marks
A circle has area \(289\pi\) square cm. A second has four times this area. How do the radii compare?
Hint
Take the positive square root of the area factor.
Stage 9 - Q9 - 4 marks
A circular sign must have area at least \(361\pi\) square cm. Which whole-centimetre diameters are possible?
Hint
The diameter is positive; interpret the inequality in whole centimetres.
Stage 9 - Q10 - 5 marks
Challenge: Two circular pools have total area \(245\pi\) square metres. The larger radius is twice the smaller radius. Find both radii and the total circumference.
Hint
The area ratio is the square of the radius ratio.