



 
Hi Ainslie. You are asked to find the ratio (call it R) of the surface area of the cuboid to that of the sphere:
The formulas for the surface areas of the cuboid and the sphere are easy:
To find the surface area of the sphere, we will need to determine its radius r (you can see it represented faintly in the diagram. Since r is also the distance from the geometric center of the golden cuboid to a corner, we can use the distance formula to find r. Now you have all the pieces you need to assemble the solution, Ainslie. Substitute for r and simplify. Hope this helps,  


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