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
[tex]$V_{1}=\frac{1}{3} \cdot b \cdot h$[/tex]
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,
[tex]b=2b[/tex] and [tex]h=2h[/tex]
Thus, volume of the triangular pyramid is given by
[tex]$V_{2}=\frac{1}{3} \cdot2b \cdot 2h$[/tex]
Multiplying, we get,
[tex]$V_{2}=\frac{1}{3}4bh[/tex]
[tex]$V_{2}=4\frac{1}{3}bh[/tex]
[tex]V_2$=4 \cdot V_{1}$[/tex]
Thus, doubling all the dimensions of a triangular pyramid, the volume of the pyramid becomes quadrupled.
