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BECE Mathematics 2010 Paper

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Question : 25

Total: 40

Find the circumference of a circle whose area is equal to

64 \pi \text{ cm}^2

$32 \pi \text{ cm}$
$16 \pi \text{ cm}$
$8 \pi \text{ cm}$
$4 \pi \text{ cm}$

Solution:

Circumference of a circle

=2 \pi r

Area of a circle

=\pi r^2

Where

r=

radius of the circle.

But area

=64 \pi \text{ cm}^2

\pi r^2=64 \pi \text{ cm}^2

\pi

cancels each other

r^2=64 \text{ cm}^2

64 \text{ cm}^2=8 \text{ cm} \times 8 \text{ cm}

64 \text{ cm}^2=(8 \text{ cm})^2

r^2=(8 \text{ cm})^2

Since the powers are the same, the bases are also the same.

r=8 \text{ cm}

Circumference of a circle

=2 \pi \times 8 \text{ cm}

Circumference of a circle

=16 \pi \text{ cm}

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