1. **Problem 5: Find the circumference and area of the circle with radius $\sqrt{2}$ cm.** 2. The formulas for circumference and area of a circle are: $$\text{Circumference} = 2\pi r$$ $$\text{Area} = \pi r^2$$ where $r$ is the radius. 3. Given $r = \sqrt{2}$ cm, substitute into the formulas: $$\text{Circumference} = 2\pi \times \sqrt{2} = 2\pi\sqrt{2}$$ $$\text{Area} = \pi (\sqrt{2})^2 = \pi \times 2 = 2\pi$$ 4. So, the circumference is $2\pi\sqrt{2}$ cm and the area is $2\pi$ cm$^2$. 5. **Problem 6: Noor slices through a circular cake with diameter 14 inches. The slice length is 11 inches. Determine if the slice is along a radius, diameter, or chord.** 6. The radius is half the diameter: $$r = \frac{14}{2} = 7$$ 7. The slice length is 11 inches, which is not equal to the radius (7) or diameter (14). 8. Since the slice length is less than the diameter but greater than the radius, it must be a chord. 9. The chord length $c$ can be related to the radius and the perpendicular distance $d$ from the center by: $$c = 2\sqrt{r^2 - d^2}$$ 10. Since the slice length is 11, it is a chord, not a radius or diameter. **Final answers:** - Circumference = $2\pi\sqrt{2}$ cm - Area = $2\pi$ cm$^2$ - Noor cut along a chord of the circle.