Posted: 3/31/2011 9:31:19 PM EDT
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I'm a freshman engineering major taking calculus, but a problem in my high school sister's homework stumped me. The problem is a triangular pyramid with volume of 18sqrt(3). The height of the pyramid is 6. The base is an equilateral triangle, sides equal to x. What is the value of x? I feel like I'm over complicating it somehow because I'm making it harder than what I think it should be. ETA:  ETA2: Apparently I was doing something wrong in finding the area of the base. I tried another formula for the area of an equilateral triangle and it took about a whole minute to find that x=6. |
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The volume of any pyramid (according to google) is the area of the base * height * 1/3; so if the volume = 18 (3^(1/2)) and height = 6; then (area) * 6 * 1/3=18(sqrt3) =>area of the triangle is 9(sqrt3) and since (according to google) the area of an equilateral triangle = s(sqrt3)/4; where s is a side; 9sqrt3 = s (sqrt3)/4; x then = 36
Prep Double check the math but the formulas should at least be correct |
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Quoted: The volume of any pyramid (according to google) is the area of the base * height * 1/3; so if the volume = 18 (3^(1/2)) and height = 6; then (area) * 6 * 1/3=18(sqrt3) =>area of the triangle is 9(sqrt3) and since (according to google) the area of an equilateral triangle = s(sqrt3)/4; where s is a side; 9sqrt3 = s (sqrt3)/4; x then = 36 Prep Double check the math but the formulas should at least be correct This looks right |
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Volume of a pyramid V = base_area * height * 1/3
in this case we have: V = 18 sqrt(3) 18 sqrt(3) = height * base_area * 1/3 height is given as 6 18sqrt(3) = base_area * 6 * 1/3 simplifying step 1 (6 * 1/3 = 2) 18sqrt(3) = base_area * 2 simplifying step 2 (divide by 2) 9sqrt(3) = base_area So now we solve for the area of an equilateral triangle. The formula for area of equilateral triangle of side length s is: s^2 sqrt(3) / 4 substituing x for s (to match the problem) and 9qrst(3) for base area (solved from previous step): 9 sqrt(3) = x^2 *sqrt(3) / 4 simplify: divide both sides by sqrt(3) (not showing this, just result) 9 = x^2 / 4 simplyfy, multiply both sides by 4: 9*4 = x^2 Simplify: 36 = x^2 x = sqrt(36) x = 6 |
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Quoted:
You've got the first right answer, seek. I had a hard ass geometry and calculus teacher in school, 30 years later I still show my work  .
I do more advanced math for my work, most of the time spent was writing this out, damn some folks type fast here and I'm no slouch. |