1. Calculate the surface area of a sphere of radius 6 cm. The formula for the surface area $A$ of a sphere is given by: $$A = 4\pi r^2$$ where $r$ is the radius. Step 1: Substitute $r = 6$ cm into the formula. $$A = 4\pi (6)^2$$ Step 2: Calculate the square of the radius. $$6^2 = 36$$ Step 3: Calculate the surface area. $$A = 4\pi \times 36 = 144\pi \, \text{cm}^2$$ Hence, the surface area of the sphere is $144\pi$ cm$^2$ or approximately $452.39$ cm$^2$. --- 2. Calculate the curved surface area of a hemispherical bowl with radius 4.5 cm. The curved surface area $A_{hemisphere}$ of a hemisphere is half the surface area of a full sphere, plus the circular base is not part of the curved surface, so the curved surface area is: $$A_{hemisphere} = 2\pi r^2$$ Step 1: Substitute $r = 4.5$ cm. $$A_{hemisphere} = 2\pi (4.5)^2$$ Step 2: Square the radius. $$4.5^2 = 20.25$$ Step 3: Calculate the curved surface area. $$A_{hemisphere} = 2\pi \times 20.25 = 40.5\pi \, \text{cm}^2$$ Hence, the curved surface area of the hemispherical bowl is $40.5\pi$ cm$^2$ or approximately $127.23$ cm$^2$. --- 3. Find the volume of a sphere with diameter 8 m. First, find the radius $r$: $$r = \frac{\text{diameter}}{2} = \frac{8}{2} = 4 \, m$$ The volume $V$ of a sphere is given by: $$V = \frac{4}{3}\pi r^3$$ Step 1: Substitute $r=4$ m into the formula. $$V = \frac{4}{3}\pi (4)^3$$ Step 2: Calculate $4^3$. $$4^3 = 64$$ Step 3: Calculate the volume. $$V = \frac{4}{3}\pi \times 64 = \frac{256}{3}\pi \, \text{m}^3$$ Hence, the volume of the sphere is $\frac{256}{3}\pi$ m$^3$ or approximately $268.08$ m$^3$.