1. **Problem 13:** A round table cover has six equal designs. The radius of the cover is 28 cm. Find the cost of making the designs at the rate of 0.35 per cm². Use $ \sqrt{3} = 1.7 $. 2. **Step 1:** Understand the design shape. The cover is divided into 6 equal sectors, each sector is an equilateral triangle because the central angle is $ 360^\circ / 6 = 60^\circ $. 3. **Step 2:** Calculate the area of one triangular design. Each design is an equilateral triangle with side length equal to the radius $ R = 28 $ cm. The formula for the area of an equilateral triangle is: $$\text{Area} = \frac{\sqrt{3}}{4} s^2$$ where $ s = 28 $. 4. **Step 3:** Calculate the area of one design. $$\text{Area} = \frac{1.7}{4} \times 28^2 = \frac{1.7}{4} \times 784 = 0.425 \times 784 = 333.2 \text{ cm}^2$$ 5. **Step 4:** Calculate the total area of all 6 designs. $$6 \times 333.2 = 1999.2 \text{ cm}^2$$ 6. **Step 5:** Calculate the cost of making the designs. Cost rate = 0.35 per cm² $$\text{Cost} = 1999.2 \times 0.35 = 699.72$$ 7. **Answer for Problem 13:** The cost of making the designs is 699.72. --- 8. **Problem 14:** Tick the correct formula for the area of a sector of angle $ p $ degrees in a circle of radius $ R $. 9. **Step 1:** Recall the formula for the area of a sector. The area of a sector with central angle $ p $ degrees is: $$\text{Area} = \frac{p}{360} \times \pi R^2$$ 10. **Step 2:** Compare with options: - (A) $ \frac{p}{180} \times 2\pi R $ is the length of an arc, not area. - (B) $ \frac{p}{180} \times \pi R^2 $ is twice the correct fraction. - (C) $ \frac{p}{360} \times \pi R^2 $ is the correct formula. 11. **Answer for Problem 14:** Option (C) is correct.