Doubling all the dimensions of a triangular pyramid, the volume of the pyramid becomes quadrupled.
Explanation:
The volume of the triangular pyramid is given by
where b is the base of the pyramid and
h is the height of the pyramid.
Doubling all the dimensions of the pyramid, we have,
and
Thus, volume of the triangular pyramid is given by
Multiplying, we get,
Thus, doubling all the dimensions of a triangular pyramid, the volume of the pyramid becomes quadrupled.
Two triangles are similar if the only difference between them is the size, this means that their internal angles must be the same. If we look at the picture the first triangle has one angle equal to 40 degrees, one equal to 80 degrees and the third one is unkown (x). The second triangle has one angle equal to 40 degrees, one equal to 60 degrees and the third one is unkown (y). The sum of the internal angles of a triangle must be equal to 180 degrees, with this information we can find the values of the missing angles. We have:
Therefore the internal angles of the first triangle are (40,80,60) and the angles of the second triangle are (40,80,60) as well, therefore they are similar.
Two triangles are congruent if they have sides with the same length. Which is not the case, because the sides of one triangle is (8, 10, 6) while the other is (4,3 and unkown). Therefore they are not congruent.