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.
Sphere Surface Area 86E833
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