Today Puzzle #762
Puzzle No. 762鈥� Tuesday 16 June 2020
I have a small hollow sphere, a hollow cube and a large hollow sphere. They nest inside each other like Russian dolls. The small sphere fits perfectly inside the cube. The cube itself fits snuggly inside the large sphere. What it the ratio of the surface areas of the two spheres?
Today’s #PuzzleForToday has been set by Hugh Hunt, Reader in Engineering Dynamics and Vibration at Trinity College, Cambridge
Click here for the answer
3
Take the side of the cube as length 2. The small sphere touches the sides and so has radius 1. The large sphere touches the corners and so has radius sqrt(3) , ie half the length of the diagonal of the cube.
Surface area goes as the radius squared so the big sphere has 3 times the surface area of the small sphere.
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