SOLUTION: 1. The altitude of a regular square pyramid is three times its base edge. The volume of the pyramid is 64 cu.cm. Find the length of the base edge of the pyramid. 2. What is the v

Algebra ->  Formulas -> SOLUTION: 1. The altitude of a regular square pyramid is three times its base edge. The volume of the pyramid is 64 cu.cm. Find the length of the base edge of the pyramid. 2. What is the v      Log On


   



Question 1194980: 1. The altitude of a regular square pyramid is three times its base edge.
The volume of the pyramid is 64 cu.cm. Find the length of the base edge of the pyramid.
2. What is the volume of the largest pyramid that can be cut froma blockk of cubical wood of edge 8 cm.

Answer by ikleyn(52790) About Me  (Show Source):
You can put this solution on YOUR website!
.
The altitude of a regular square pyramid is three times its base edge.
The volume of the pyramid is 64 cu.cm. Find the length of the base edge of the pyramid.
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            Of two problems of this post,  I will solve only first one.


Let x be the length og the base edge.


Then the volume of the pyramid is  %281%2F3%29%2Ax%5E2%2A%283x%29 = x^3.


Hence, the volume equation is

    x^3 = 64.


Its solution is  x = root%283%2C64%29 = 4.


ANSWER.  The length of the base edge of the pyramid is 4 centimeters.

Solved and clearly explained.


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