If the height of a triangular pyramid is doubled, what effect does this have on its volume?

The correct answer is that the volume of the triangular pyramid doubles when the height is doubled. The formula for the volume of a triangular pyramid is given by:

[

V = \frac{1}{3} \times B \times h

]

where ( V ) is the volume, ( B ) is the area of the base, and ( h ) is the height of the pyramid.

When the height ( h ) is doubled, the new height becomes ( 2h ). Substituting this into the volume formula gives:

[

V_{\text{new}} = \frac{1}{3} \times B \times (2h) = \frac{2}{3} \times B \times h

]

This shows that the new volume is twice the original volume. Therefore, the volume increases in a linear relationship with the height, meaning that if the height is doubled, the volume also doubles.

This understanding of the mathematical relationship illustrates why the volume triples, quadruples, or remains the same does not apply in this scenario. The direct correlation between height and volume reinforces the concept that altering the height alone generates a proportional increase in volume.