BECE Mathematics 2012 Paper

Concept:The curved semi-circular portion contributes half of a full circle’s circumference, which is $\frac{\pi d}{2}$, where $d$ is its diameter.Explanation:Perimeter is the total outer length of the figure.So, perimeter $= 25 \text{ cm} + 24 \text{ cm} + \frac{\pi d}{2}$.Given perimeter $= 71 \text{ cm}$.Therefore, $25 + 24 + \frac{\pi d}{2} = 71$.This gives $49 + \frac{\pi d}{2} = 71$.So, $\frac{\pi d}{2} = 71 - 49 = 22$.Multiplying both sides by $2$, we get $\pi d = 44$.Using $\pi = \frac{22}{7}$, we have $\frac{22}{7} d = 44$.Hence, $d = 44 \times \frac{7}{22} = 14$ cm.Answer:The diameter of the semi-circumference portion is $14.0$ cm.Correct option: D. $14.0$ cm.