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Geometry
Level
3
I bought a transparent pyramid with the base of 6×6 square. The height of this pyramid is 4. Then, I decided to place a sphere as a decoration in it. I got one and I realised that the sphere touches all surfaces of the pyramid. What is the radius of the sphere?
The answer is 1.5.
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1 solution
This is part of geometry circle properties. Actually using pythagoras theorem gives you the the length 5, 5^{2}=3^{2}+4^{2}
The area of one of the triangle from pyramid= radius × the perimeter÷2 6×4÷2=r×(5++5+6) r=1.5