1. **State the problem:** We have a square pizza box with an 8-slice circular pizza inside. The box's side length is 5 cm longer than the pizza's diameter. The area of the box's top is 784 cm². We need to find: (a) The radius of the pizza. (b) The area of one slice of pizza. 2. **Formulas and rules:** - Area of a square: $$A = s^2$$ where $s$ is the side length. - Diameter of pizza: $$d = 2r$$ where $r$ is the radius. - Side length of box: $$s = d + 5 = 2r + 5$$ - Area of circle (pizza): $$A_{pizza} = \pi r^2$$ - Area of one slice: $$\frac{A_{pizza}}{8}$$ 3. **Find the side length of the box:** Given $$A = 784$$, $$s^2 = 784$$ $$s = \sqrt{784} = 28$$ cm 4. **Relate side length to radius:** $$s = 2r + 5$$ $$28 = 2r + 5$$ Subtract 5 from both sides: $$28 - 5 = 2r$$ $$23 = 2r$$ Intermediate step with cancellation: $$23 = \cancel{2}r / \cancel{2}$$ Divide both sides by 2: $$r = \frac{23}{2} = 11.5$$ cm 5. **Calculate area of pizza:** $$A_{pizza} = 3.14 \times (11.5)^2 = 3.14 \times 132.25 = 415.265$$ cm² 6. **Calculate area of one slice:** $$\frac{415.265}{8} = 51.908125$$ cm² **Final answers:** (a) Radius of pizza: $11.5$ cm (b) Area of one slice: approximately $51.91$ cm²