1. **Problem statement:** We have a table with a circular top and a circular base. (a) Find the area of the top of the table with radius 50 cm. (b) Find the circumference of the base of the table with diameter 40 cm. 2. **Formulas and rules:** - Area of a circle: $$A = \pi r^2$$ where $r$ is the radius. - Circumference of a circle: $$C = 2 \pi r$$ or equivalently $$C = \pi d$$ where $d$ is the diameter. 3. **Part (a) Area of the top:** - Given radius $r = 50$ cm. - Substitute into area formula: $$A = \pi \times 50^2 = \pi \times 2500$$ - Calculate: $$A = 2500\pi$$ - Using $\pi \approx 3.1416$: $$A \approx 2500 \times 3.1416 = 7854$$ - The area is approximately 7853.98 cm$^2$ (rounded to two decimal places). 4. **Part (b) Circumference of the base:** - Given diameter $d = 40$ cm. - Use circumference formula: $$C = \pi d = \pi \times 40$$ - Calculate: $$C = 40\pi$$ - Using $\pi \approx 3.1416$: $$C \approx 40 \times 3.1416 = 125.664$$ - The circumference is approximately 125.66 cm. **Note:** The user provided 251.32 for circumference, which corresponds to $2\pi d$ or $4\pi r$, but circumference is $\pi d$ or $2\pi r$. So the correct circumference is about 125.66 cm. **Final answers:** - Area of top: 7853.98 cm$^2$ - Circumference of base: 125.66 cm