Area & volumeStructured · 5 marks

A rectangular metal plate measures 45 cm by 34 cm. Four identical quarter circles are cut away, one at each corner of the plate. The centre of each quarter circle is at a corner of the plate. On each longer side, the straight edge left between the two cut corners is 17 cm long. (Take π = 3.14)

Find the radius of each quarter circle.
Find the perimeter of the plate that is left.
Find the area of the plate that is left.

Need a hint?

Along a longer side you see: radius, a straight 17 cm piece, radius. Four quarter circles together make one whole circle.

Worked answer

(a) The 45 cm side = radius + 17 cm + radius, so 2 radii = 45 − 17 = 28 cm.
Radius = 28 ÷ 2 = 14 cm.
(b) The 4 curved edges together make one whole circle: 2 × 3.14 × 14 = 87.92 cm.
Straight edges on the long sides: 2 × 17 = 34 cm.
Each short side keeps 34 − 14 − 14 = 6 cm, so the 2 short sides give 12 cm.
Perimeter = 87.92 + 34 + 12 = 133.92 cm.
(c) Area of the rectangle = 45 × 34 = 1530 cm².
The 4 quarter circles make one whole circle: 3.14 × 14 × 14 = 615.44 cm².
Area of the plate left = 1530 − 615.44 = 914.56 cm².

Answer: 914.56 cm²

The mistake this question tests

Habit

Radius and diameter in circles

Many pupils use 28 cm as the radius because they forget that the 28 cm covers two radii. Others find the perimeter by adding the arcs to the full rectangle perimeter instead of replacing the cut-away corner edges.

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