Subjects geometry

Kolam Ikan

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1. **Stating the problem:** We have a circular park with radius $r=14$ meters. Inside it, there is a fish pond shaped as a circular sector (juring) with central angle $\alpha=90^\circ$. We need to find: - The arc length (Panjang Busur, PB) of the sector. - The area (Luas Juring, LJ) of the sector. 2. **Formulas and rules:** - Arc length of a sector: $$PB = \frac{\alpha}{360^\circ} \times 2\pi r$$ - Area of a sector: $$LJ = \frac{\alpha}{360^\circ} \times \pi r^2$$ Note: $\pi \approx 3.1416$ and angles must be in degrees. 3. **Calculating the arc length:** $$PB = \frac{90}{360} \times 2 \times 3.1416 \times 14 = \frac{1}{4} \times 2 \times 3.1416 \times 14$$ $$PB = \frac{1}{4} \times 87.9648 = 21.9912 \text{ meters}$$ 4. **Calculating the area of the sector:** $$LJ = \frac{90}{360} \times 3.1416 \times 14^2 = \frac{1}{4} \times 3.1416 \times 196$$ $$LJ = \frac{1}{4} \times 615.752 = 153.938 \text{ square meters}$$ **Final answers:** - Panjang Busur (arc length) $PB \approx 21.99$ meters - Luas Juring (area) $LJ \approx 153.94$ square meters