The diagram is a square of side 2 cm in which is inscribed a circle with center {O}. Use the information to answer the question below. Find the area of the shaded portion. [Take π=22/7 ]

Correct Answer is : 0.86 cm2\;\;0.86\;{cm}²0.86cm2

Correct Answer is : 0.86 cm2\;\;0.86\;{cm}²0.86cm2

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BECE Mathematics 2023 Paper

Question : 29

Total: 40

\mathrm{O}

\pi=\frac{22}{7}

Solution:

The area of the shaded portion = Area of the square - Area of the circle

\;\;\text{Area of square}\;=\;\text{Length}\; \times \;\text{Length}\;

\;\;\text{Area of square}\;=2\;\mathrm{cm}\times 2\;\mathrm{cm}

\;\;\text{Area of square}\;=4\;\mathrm{cm}^2

Area of a circle

=\pi r^2

Where

r=

radius

Diameter of the circle

=2\;\mathrm{cm}

Radius is half the diameter

\;\;\text{Radius}\;=\;\frac{2\;\mathrm{cm}}{2}=1\;\mathrm{cm}

\;\pi=\;\frac{22}{7}

\;r=1\;\mathrm{cm}

\;r^2=r\times r

Area of the circle

=\;\frac{22}{7}\times 1\;\mathrm{cm}\times 1\;\mathrm{cm}=3.14\;\mathrm{cm}^2

Area of the shaded portion

=4\;\mathrm{cm}^2-3.14\;\mathrm{cm}^2

Area of the shaded portion

=0.86\;\mathrm{cm}^2

22 divided by 7

3.1428\approx 3.14

(2 decimal places)

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