Question 1034963: Construct a triangular pyramid with a surface area between 1800 and 2100 square centimeters and a volume between 4000 and 4500 cubic centimeters. What are the dimensions of the triangular pyramid?
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! Let's find you a pyramid made of four equilateral triangles with a total area of 1800
A triangular pyramid has 4 faces (triangles). Let each triangle be:
2000/4 = 450 is the area for each triangle
Area of the triangle:
1/2bh = 450 Since the sides of an equilateral triangle are identical, we can re-write the equation:
1/2(b^2) = 450, b^2/2 = 450, b^2 = 900, b = 30 NOTE This is our Base as well as our Height.
Proof:
Area of the triangle:
1/2bh
1/2(30*30)= 450 Correct
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Now that we have the area of the sides, we can calculate the volume:
1/3(Area*height)= Volume
1/3(450*30)= 4500 is your volume
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and there you have it.
John
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