1. **State the problem:** We have a circular plate with circumference $c = 50.24$ cm and a rectangular tray with dimensions $35$ cm by $50$ cm. We want to find how many plates can fit on the tray. 2. **Find the radius of the circular plate:** The circumference formula is $$c = 2\pi r$$ where $r$ is the radius. 3. **Calculate the radius:** $$r = \frac{c}{2\pi} = \frac{50.24}{2\pi}$$ 4. **Calculate the radius value:** $$r = \frac{50.24}{2 \times 3.1416} = \frac{50.24}{6.2832} \approx 8$$ cm 5. **Find the diameter of the plate:** $$d = 2r = 2 \times 8 = 16$$ cm 6. **Determine how many plates fit on the tray:** - The tray is $35$ cm by $50$ cm. - Each plate occupies a square of side $16$ cm (since plates are circular, we consider diameter for fitting). 7. **Calculate how many plates fit along each dimension:** $$\text{plates along width} = \left\lfloor \frac{35}{16} \right\rfloor = \left\lfloor 2.1875 \right\rfloor = 2$$ $$\text{plates along length} = \left\lfloor \frac{50}{16} \right\rfloor = \left\lfloor 3.125 \right\rfloor = 3$$ 8. **Calculate total plates that fit:** $$2 \times 3 = 6$$ plates **Final answer:** 6 plates will fit on the tray.