Practice Maths

Topic Review — Circles

Mixed Practice — L28 – L30

This review covers all lessons in the Circles topic. Try each question before checking your answers. Use π ≈ 3.14 unless told otherwise, or give exact answers in terms of π.

Review Questions

  1. Parts of a circle and circumference. Fluency

    1. Name the part of a circle that: (i) is a line from the centre to the edge (ii) passes through the centre joining two points on the circle (iii) is a portion of the circumference.
    2. Find the circumference of a circle with radius 7 cm. Give your answer in terms of π and as a decimal (use π ≈ 3.14).
    3. Find the circumference of a circle with diameter 15 m. Give your answer correct to 2 decimal places.
    4. A circle has circumference 62.8 cm. Find the radius.
    5. A circular running track has diameter 80 m. How far does an athlete run if they complete 5 laps? Give your answer correct to the nearest metre.
    6. Find the perimeter of a semicircle with diameter 12 cm. Include the straight edge.

  2. Area of a circle. Fluency

    1. Find the area of a circle with radius 5 cm. Give your answer in terms of π and as a decimal.
    2. Find the area of a circle with diameter 18 m. Give your answer correct to 2 decimal places.
    3. A circle has area 154 cm². Find the radius (use π ≈ 22/7).
    4. Find the area of a circle with radius 3.5 m. Give your answer correct to 2 decimal places.
    5. Find the area of a semicircle with diameter 20 cm.
    6. A circle has area 200π mm². Find the exact radius in simplest surd form.

  3. Arc length and sector area. Understanding

    1. Find the arc length of a sector with radius 9 cm and angle 120°. Give your answer in terms of π.
    2. Find the arc length of a sector with radius 6 m and angle 270°. Give your answer correct to 2 decimal places.
    3. Find the area of a sector with radius 10 cm and angle 72°. Give your answer in terms of π.
    4. Find the area of a sector with radius 8 m and angle 45°. Give your answer correct to 2 decimal places.
    5. A sector has arc length 10π cm and radius 15 cm. Find the angle of the sector.
    6. A sector has area 24π cm² and radius 12 cm. Find the angle of the sector.

  4. Mixed circle calculations. Understanding

    1. A quarter-circle (quadrant) has radius 14 cm. Find: (i) the arc length (ii) the perimeter (including straight edges) (iii) the area.
    2. A circle is inscribed in a square (fits perfectly inside). The square has side 10 cm. Find the area of the square NOT covered by the circle.
    3. Two concentric circles (same centre) have radii 5 cm and 8 cm. Find the area of the ring between them.
    4. A circle has radius r cm and its area equals its circumference numerically. Find r.

  5. Circle problem solving. Problem Solving

    1. A pizza has diameter 32 cm. It is cut into 8 equal slices. Find: (i) the arc length of one slice (ii) the area of one slice. Give answers correct to 2 decimal places.
    2. A circular sprinkler waters a region of radius 6 m. What area does it cover? If a second sprinkler with radius 4 m is placed so the two circles do not overlap, what total area is covered by both? Give answers in terms of π.
    3. The wheel of a bicycle has diameter 70 cm. How many complete rotations does the wheel make if the cyclist travels 1 km? (Use π ≈ 3.14.)
    4. A sector of a circle has radius 12 cm and angle 150°. A student says its area is “the same as a circle with radius 12 cm divided by 2.5”. Is the student correct? Show your working and explain.
See Answers ➔