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BECE Mathematics 2023 Paper

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Question : 30

Total: 40

The diagram is a square of side 2 cm in which is inscribed a circle with center

\mathrm{O}

. Use the information to answer the question below.

Find the area of the circle.

\pi=\frac{22}{7}

$3.14\,\mathrm{cm}^2$
$6.28\,\mathrm{cm}^2$
$4.00\,\mathrm{cm}^2$
$12.56\,\mathrm{cm}^2$

Solution:

Concept:

For a circle inscribed in a square, the diameter of the circle is equal to the side of the square.

Explanation:

Side of the square

= 2\,\mathrm{cm}

.

So, diameter of the circle

= 2\,\mathrm{cm}

.

Radius

= \frac{\text{diameter}}{2} = \frac{2\,\mathrm{cm}}{2} = 1\,\mathrm{cm}

.

Area of a circle

= \pi r^2

.

Substitute

\pi = \frac{22}{7}

and

r = 1\,\mathrm{cm}

:

Area

= \frac{22}{7} \times (1\,\mathrm{cm})^2 = \frac{22}{7}\,\mathrm{cm}^2

.

\frac{22}{7} = 3.1428 \ldots \approx 3.14\,\mathrm{cm}^2

.

Hence, the area of the circle is approximately

3.14\,\mathrm{cm}^2

.

Answer:

A.

3.14\,\mathrm{cm}^2

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