SOLUTION: The volume of a square pyramid whose slant height and base edge are each 10.ft long may be expressed as V = γ√ρ/ρ ft.^2 where ρ is a prime number. Find γ - ρ.

Algebra ->  Polygons -> SOLUTION: The volume of a square pyramid whose slant height and base edge are each 10.ft long may be expressed as V = γ√ρ/ρ ft.^2 where ρ is a prime number. Find γ - ρ.       Log On


   

Question 1198262: The volume of a square pyramid whose slant height and base edge are each 10.ft long may be expressed as V = γ√ρ/ρ ft.^2 where ρ is a prime number. Find γ - ρ.
Answer by ikleyn(52802) About Me  (Show Source):
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The volume of a square pyramid whose slant height and base edge are each 10 ft long
may be expressed as V = γ√ρ/ρ ft.^2 where ρ is a prime number. Find γ - ρ.
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The base area is 10*10 = 100 ft^2.


The height of the pyramid is  sqrt%2810%5E2-%2810%2F2%29%5E2%29 = sqrt%28100-25%29 = sqrt%2875%29 = 5%2Asqrt%283%29.


The volume of the pyramid is  %281%2F3%29%2A5%2Asqrt%283%29 = 5%2A%28sqrt%283%29%2F3%29 ft^3.


So we have γ = 5, ρ = 3.  Therefore,  γ - ρ = 5 - 3 = 2.    ANSWER

Solved.