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?

1 Answer
May 8, 2018

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