1. **Problem Statement:** Find the volume and total surface area (TSA) of a sphere with a radius of 4 cm. 2. **Formulas:** - Volume of a sphere: $$V = \frac{4}{3} \pi r^3$$ - Total surface area of a sphere: $$A = 4 \pi r^2$$ 3. **Given:** Radius $r = 4$ cm. 4. **Calculate Volume:** $$V = \frac{4}{3} \pi (4)^3 = \frac{4}{3} \pi (64) = \frac{256}{3} \pi \text{ cm}^3$$ 5. **Calculate Total Surface Area:** $$A = 4 \pi (4)^2 = 4 \pi (16) = 64 \pi \text{ cm}^2$$ 6. **Final answers:** - Volume: $$\frac{256}{3} \pi \text{ cm}^3$$ - Total Surface Area: $$64 \pi \text{ cm}^2$$