(a) (i) The height of each cone is equal to the diameter of its base. If the radius of the base is 2.25 m , write the height of a cone. (ii) Show that, correct to two decimal places, the slant height, \( l \), of a cone is 5.03 m . (b) In order to maintain the steel's reflective shine, the surface is polished regularly. (i) Find the curved surface area of the entire sculpture ( 14 cones). Give your answer correct to two decimal places. (ii) One litre of polish will cover \( 12 \cdot 25 \mathrm{~m}^{2} \). Find how many litres are needed to polish the entire sculpture. Give your answer correct to the nearest litre.

For each cone, if the radius is 2.25 m, the diameter is \(2 \times 2.25 = 4.5\) m, meaning the height of the cone is simply 4.5 m, since the problem states that the height is equal to the diameter of its base. Next, to find the slant height \( l \), we can use the Pythagorean theorem. The formula for the slant height \( l \) is \( l = \sqrt{r^2 + h^2} \). Plugging in the values \( r = 2.25 \) m and \( h = 4.5 \) m, we find \( l = \sqrt{(2.25)^2 + (4.5)^2} = \sqrt{5.0625 + 20.25} = \sqrt{25.3125} \approx 5.03 \) m when rounded to two decimal places. For the curved surface area of one cone, the formula is given by \( CSA = \pi r l \) where \( r \) is the radius and \( l \) is the slant height. So, plugging in the numbers for one cone gives us \( CSA = \pi \times 2.25 \times 5.03 \approx 35.52 \) m². Multiplying this by 14 for all cones results in approximately \( 497.28 \text{ m}^2 \). To find how many litres of polish are needed, we divide the total curved surface area \( 497.28 \text{ m}^2 \) by the coverage of one litre of polish \( 12.25 \text{ m}^2 \). This results in about \( 40.6 \) litres of polish required. Rounding to the nearest litre, you will need approximately 41 litres of polish to keep your sculpture shining bright!