Re: Eliminate

On Fri, 24 Apr 2009 21:22:42 EDT, KY <wkfkh056@xxxxxxxxxxx> wrote:

Eliminate L and t ;
V = 1/3*(-a + b)^2*h + a^2*L*Sin[t] + 2*a*L^2*Cos[t]*Sin[t]
1/2*(-a + b)= L*Cos[t],
L^2 = 1/4*(-a + b)^2 + h^2
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http://mathworld.wolfram.com/TruncatedSquarePyramid.html

I assume you want to show that
V = h/3 (a^2 + ab + b^2)

Using the second equation,
(b-a)^2 / 4 = L^2 cos[t]^2

Substituting into the third equation,
L^2 = L^2 cos[t]^2 + h^2
L^2 (1 - cos[t]^2) = h^2
L sin[t] = h
sin[t] = h/L

In the formula for V, make the substitutions
cos[t] = (b-a)/(2L)
sin[t] = h/L

.