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Primary 6 · Circle · Question type 6.5

P6 Circle: Area Left When a Circle Is Cut from a Square

Find the remaining area by subtracting the cut-out region from the whole figure.

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Primary 6, on the MOE Primary Mathematics syllabus.

In the Circle chapter9 question types · see the chapter

The lesson · 2 minutes 24 seconds

How do you find the area left when a circle is cut from a square in P6?

Watch: the area left when a circle is cut out of a square of paper

Another worked example

A worked example

The figure shows 3 semicircles drawn on the straight line AB, where C is a point on AB. The semicircle on AB and the semicircle on CB are drawn above AB, and the semicircle on AC is drawn below AB. AB is 60 cm long and CB is twice as long as AC. Find the area of the figure. (Take π = 3.14.)

The working · Twelve lines

The step-by-step working

Written out in full, the way it should appear on paper.

  1. area of circle = π × r × r
  2. area = the semicircle on AB - the semicircle on CB + the semicircle on AC
  3. AC + CB = AB, and CB = 2 × AC, so AB is 3 equal parts of AC
  4. AC = 60 ÷ 3 = 20
  5. CB = 20 × 2 = 40
  6. radius on AB = 60 ÷ 2 = 30
  7. radius on CB = 40 ÷ 2 = 20
  8. radius on AC = 20 ÷ 2 = 10
  9. the semicircle on AB = 1/2 × 3.14 × 30 × 30 = 1413
  10. the semicircle on CB = 1/2 × 3.14 × 20 × 20 = 628
  11. the semicircle on AC = 1/2 × 3.14 × 10 × 10 = 157
  12. area = 1413 - 628 + 157 = 942

The answer is 942 cm².

Practise · Modelled on top school exam questions

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Find the difference between two regions

Identify the common overlap before finding the difference.

The figure shows a rectangle 18 cm long and 12 cm wide. A semicircle is drawn inside it with the whole of the bottom edge as its diameter, and a quarter circle of radius 12 cm is drawn inside it with its centre at the bottom right corner. The two curves cross. Region P is the part covered by the semicircle only and region Q is the part covered by the quarter circle only. Find the difference between the area of P and the area of Q. (Take π = 3.14.)

cm²

Show the step-by-step solution
  1. area = π × r × r
  2. P - Q = semicircle - quarter circle
  3. radius of the semicircle = 18 ÷ 2 = 9
  4. semicircle = 1/2 × 3.14 × 9 × 9 = 127.17
  5. quarter circle = 1/4 × 3.14 × 12 × 12 = 113.04
  6. P - Q = 127.17 - 113.04 = 14.13

Ans: 14.13 cm²

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Next, find an unlabelled length from touching shapes. Finding a Circle's Radius or Diameter from a Composite Figure →

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