Today Puzzle #564
Puzzle No. 564鈥� Tuesday 10 September
A news story broke on September 5th (/news/science-environment-49595680) where scientists reported two large holes in the skull of a Tyrannosaurus acted as a kind of internal "air-conditioning unit", to help the dinosaur lose heat. This is because large animals need special ways to cool down, since their immense body heat can overwhelm them in hot conditions. Assuming an animal is a cube and that they all have the same density, what is the increase in surface area to volume ratio for an animal of half the mass?
Today’s #PuzzleForToday has been set by Dr Shaun Fitzgerald, Director of The Royal Institution
Click here for the answer
For a cube with side length a its volume is a3. The surface area is given by 6a2. The surface area to volume ratio is therefore 6/a. The volume of the smaller animal with half the mass is 0.5a3. The side length b is 0.51/3a. The surface area to volume ratio of the smaller animal is (6b2)/ 0.5a3 = (6x0.52/3a2)/ 0.5a3 = 7.56/a. The increase in surface area to volume ratio is therefore given by (7.56/a – 6/a)/(6/a) = (7.56-6)/6 = 26%.
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