Subjects geometry

Sphere Surface Area 86E833

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1. **Problem statement:** We have a hollow spherical memorial with an outer radius of $1.2$ meters. We need to find: (a) The outer surface area. (b) The amount of paint needed to cover the outer surface if 1 litre covers 12 m². 2. **Formula for surface area of a sphere:** The surface area $A$ of a sphere with radius $r$ is given by: $$A = 4\pi r^2$$ 3. **Calculate the outer surface area:** Given $r = 1.2$ m, $$A = 4 \pi (1.2)^2 = 4 \pi (1.44) = 5.76 \pi$$ Using $\pi \approx 3.1416$, $$A \approx 5.76 \times 3.1416 = 18.1 \text{ m}^2$$ 4. **Calculate the amount of paint needed:** Coverage is 12 m² per litre, so paint needed $P$ is: $$P = \frac{\text{surface area}}{\text{coverage}} = \frac{18.1}{12} = 1.5083 \text{ litres}$$ 5. **Final answers:** (a) Outer surface area is approximately $18.1$ m². (b) Paint needed is approximately $1.51$ litres. This means you need about 1.51 litres of paint to cover the outer surface of the memorial.