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. Calculate the perimeter of the following sector. (π=3.142) (4mks)

June 27, 2026Mathematics

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Answer

\text{20.94 cm}

Step-by-step solution

2 steps

Haya Mercy, sasa picha iko wazi.

a) Kokotoa mzingo wa sekta ifuatayo. ( $\pi = 3.142$ )

Sekta ina rediasi ( $r$ ) ya 6.5 cm na pembe ( $\theta$ ) ya 70°.
Mzingo wa sekta unajumuisha urefu wa pinde (arc length) na rediasi mbili.
Fomula ya mzingo wa sekta ni: $P = \text{urefu wa pinde} + 2r$ .
Fomula ya urefu wa pinde ( $L$ ) ni $L = \frac{\theta}{360^\circ} \times 2\pi r$ .

Kokotoa urefu wa pinde.
Tunatumia $r = 6.5 \text{ cm}$ , $\theta = 70^\circ$ , na $\pi = 3.142$ .
$L = \frac{70}{360} \times 2 \times 3.142 \times 6.5$ $L = \frac{7}{36} \times 2 \times 3.142 \times 6.5$ $L = \frac{14 \times 3.142 \times 6.5}{36}$ $L = \frac{285.922}{36}$ $L \approx 7.942 \text{ cm}$
Kokotoa mzingo wa sekta.
Mzingo ( $P$ ) = Urefu wa pinde + $2 \times \text{rediasi}$
$P = 7.942 + (2 \times 6.5)$ $P = 7.942 + 13$ $P = 20.942 \text{ cm}$
Mzingo wa sekta ni $\text{20.94 cm}$ .