The Atomium in Brussels is one of Belgium's most famous landmarks - Leaving Cert Mathematics - Question 1 - 2018

The diameter of each sphere is given as 18 metres. The radius (r) can be calculated as:

$r = \frac{diameter}{2} = \frac{18}{2} = 9 \text{ metres}$

The volume (V) of a sphere is calculated using the formula:

$V = \frac{4}{3} \pi r^3$

Substituting $r = 9$:

$V = \frac{4}{3} \pi (9)^3 = \frac{4}{3} \times 3.14 \times 729 \approx 3053.63 \text{ m}^3$

Thus, the volume is approximately 3053.63 m³.

The surface area (A) of a single sphere is given by:

$A = 4 \pi r^2$

Using $r = 9$:

$A = 4 \pi (9)^2 = 4 \times 3.14 \times 81 \approx 1021.76 \text{ m}^2$

Thus, for 9 spheres, the total surface area is:

$Total\, A = 9 \times 1021.76 \approx 9195.84 \text{ m}^2 \approx 9196 ext{ m}^2$

The curved surface area (CSA) of a single cylinder is calculated using:

$CSA = 2 \pi r h$

For each pipe, where $r = 1.65$ and $h = 23$:

$CSA = 2 \pi (1.65) (23) \approx 607.57 \text{ m}^2$

For 8 pipes:

$Total\, CSA = 8 \times 607.57 \approx 4860.56 \text{ m}^2 \approx 1909 ext{ m}^2$

The sum of the curved surface areas of the 12 pipes is given as 3170 m². To find the length (L) of one pipe:

$CSA_{12} = 12 \times 2 \pi (1.45) L = 3170$

This gives:

$L = \frac{3170}{(12 \times 2 \times 3.14 \times 1.45)} \approx 29 ext{ m}$

The total surface area to be resurfaced consists of 20 pipes and 9 spheres:

$Total\, S.A. = 3170 + 9196 = 12366 ext{ m}^2$

The cost of the stainless steel is:

$Cost = 12366 \times 70 \approx 865620 €$