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BECE Mathematics 2013 Paper

Question : 20

Total: 40

154 \mathrm{cm}^2

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

Solution:

Concept:

The area of a circle is given by

\pi r^2

, where

r

is the radius.

The diameter is twice the radius, so after finding

r

, multiply by

2

Explanation:

Given area

= 154\ \mathrm{cm}^2

and

\pi = \frac{22}{7}

Use the formula:

\text{Area} = \pi r^2

So,

154 = \frac{22}{7} \times r^2

Multiply both sides by

7

to remove the denominator:

154 \times 7 = 22 \times r^2

This gives

1078 = 22r^2

Divide both sides by

22

r^2 = \frac{1078}{22} = 49

Therefore,

r = \sqrt{49} = 7\ \mathrm{cm}

Now, diameter

= 2r = 2 \times 7 = 14\ \mathrm{cm}

Answer:

The diameter is

14\ \mathrm{cm}

, which is option B.

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