SOLUTION: The volume of a pyramid is given by the formula V = Bh / 3 where B is the area of its base and h is its height. The volume of the following pyramid is 252 cubic centimeters

Algebra ->  Trigonometry-basics -> SOLUTION: The volume of a pyramid is given by the formula V = Bh / 3 where B is the area of its base and h is its height. The volume of the following pyramid is 252 cubic centimeters      Log On


   

Question 999628: The volume of a pyramid is given by the formula V = Bh / 3
where B is the area of its base and h is its height. The volume of the following pyramid is 252 cubic centimeters. Find the dimensions of its rectangular base if one edge of the base is 2 centimeters longer than the other and the height of the pyramid is 12 centimeters. (Enter your answers as a comma-separated list.)
Found 2 solutions by ikleyn, addingup:
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.
First, find the pyramids base area.
For it, use the given volume and the height.

Since V = %28B%2Ah%29%2F3, you have B = %283%2AV%29%2Fh = %283%2A252%29%2F12 = 63 cm%5E2.

Now, for the length of the shorter edge of the base you have an equation

x*(x+2) = 63.

Solve this quadratic equation, using the quadratic formula, or the Viete's theorem, or factorization method.

The solution is x = 7 cm.


Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
V= Bh/3 but we want to find the area of the Base. Let's isolate the Base, multiply both sides by 3:
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V*3= Bh Now divide both sides by h:
(V*3)/h= B
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OK, now let's plug in the numbers provided in the problem:
(252*3)/12= B
756/12= B
B= 63 Now factor 63: It's divisible by 1, 7, 9. 7*9= 63 and 9= 7+2 so the base of your pyramid is 7*9.