The horizontal base of a solid prism is an equilateral triangle of side x the sides of the prism are vertical the height of prism is h and volume=2000 Express h in term of x show that total surface area A =(3^1/2)/2*x^2 +(24000/3^1/2)x^-1?

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Answer 1 · 2018-05-08T15:35:27

Volume for the prism is Base Area times the Height.
So we substitute our values in the equation as follows;
# V = (1/2 * x * x * sin60)#

#2000 = (1/2 * x^2 * sin60)#

#2000 = sqrt(3)/4 . x^2 h#

# 8000/sqrt(3). x^2 = h#

Now that we have our #h# let's find Surface Area;
#A = 3(h.x) + 2(1/2 .a. b. sin 60)#

#= 3hx + x^2sin60#

#3(8000/(sqrt(3)x^2))#. # x + sqrt(3)/2.x^2#

#24000/sqrt(3)x^-1 + sqrt(3)/2 x^2#