From each of the two opposite corners of a square of side 8cm, a quadrant of a circle of radius 1.4cm is cut. Another circle of radius 4.2cm is also cut from the centre as shown in Fig.15.71. Find the area of the remaining (shaded) portion of the square..

Question

From each of the two opposite corners of a square of side 8cm, a quadrant of a circle of radius 1.4cm is cut. Another circle of radius 4.2cm is also cut from the centre as shown in Fig.15.71. Find the area of the remaining (shaded) portion of the square.

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Philoid · Accepted Answer

Given,

Side of square = 8cm

Radius of quadrant circle = 1.4 cm

Radius of inner-circle = 4.2

Area of square = (side)² = 8² = 64cm

Area of one quadrant of circle =

So,

Area of 2 quadrant = 2×1.54 = 3.08cm²

Area of inner circle = πr² = 3.14×4.2×4.2 = 55.44 cm²

Area of shaded portion = area of square – (area of quadrants + area of inner circle)

= 64 – (3.08 + 55.44)

= 64 – 58.52 = 5.48 cm²