The metal used to make a sphere costs £4320. The metal costs £3.60 per gram. Each cubic centimetre of metal has a mass of 17.3 grams. Work out the radius, r, of the sphere. The volume of a sphere is given by V = (4/3)πr³.

This problem requires us to work backwards from the cost to find the radius. Step 1: Find the total mass of the metal. We know the total cost (£4320) and the cost per gram (£3.60). Total Mass = Total Cost / Cost per gram Total Mass = 4320 / 3.60 = 1200 g. Step 2: Find the volume of the sphere. We know the total mass (1200 g) and the density (17.3 g/cm³). Volume = Total Mass / Density Volume = 1200 / 17.3 = 69.36416... cm³. It's important to keep this value unrounded in your calculator for the next step. Step 3: Use the volume formula to find the radius. The formula for the volume of a sphere is V = (4/3)πr³. We substitute our calculated volume: 69.36416... = (4/3)πr³ Now, we rearrange to solve for r: - Multiply by 3: 69.36416... × 3 = 4πr³ => 208.0924... = 4πr³ - Divide by 4π: r³ = 208.0924... / (4π) => r³ = 16.561... Step 4: Find r. To find r, we take the cube root of r³: r = ³√(16.561...) r = 2.549... cm Rounding to 3 significant figures, the radius is 2.55 cm.