Each of the eight edges of a regular square pyramid has length 6. Find the volume of the pyramid.
The height of an equilateral trial=6^2 - (6/2)^2 =sqrt(27)=~5.2
Volume=(H. S^2) / 3
Volume=(5.2 x 6^2) / 3
Volume=62.4 Cubic units.
CPhill: Please verify this. Thanks.
+23251 The formula for the volume of a pyramid is: V = (1/3)·(Area of the base)·(height of the pyramid).
Since all the base of the pyramid is a square whose sides are each 6 ---> Area of the base = 36
To find the height of the pyramid, use the right triangle whose endpoints are one of the corner points of the base, the center of the base, and the top point of the pyramid.
The hypotenuse of this triangle is an edge of the pyramid = 6.
The side that connects one of the corner points of the base to the center of the base is one-half the distance from one of the corner points of the base to the corner point that is directly opposite it on the base.
Since the base is a square whose sides each equal 6, using the Pythagorean Theorem, we can find the distance from one of the corner points to its opposite corner point is 6·sqrt(2).
So the distance from a corner point to the middle of the base is 3·sqrt(2).
To find the height of the pyramid, use the Pythagorean Theorem with one side = 3·sqrt(2) and the hypotenuse = 6, so that the other side (the height of the pyramid) is 3·sqrt(2).
The volume is: V = (1/3)(36)(3·sqrt(2)) = 36·sqrt(2)
