Question

What effect would doubling all the dimensions of a triangular pyramid have on the volume of the pyramid? Explain your reasoning.

Answer 1

Answer:

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Step-by-step explanation:

Answer 2

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

$V_{1}=\frac{1}{3} \cdot b \cdot h$

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,

$b=2b$ and $h=2h$

Thus, volume of the triangular pyramid is given by

$V_{2}=\frac{1}{3} \cdot2b \cdot 2h$

Multiplying, we get,

$V_{2}=\frac{1}{3}4bh$

$V_{2}=4\frac{1}{3}bh$

$V_2 =4 \cdot V_{1}$

Thus, doubling all the dimensions of a triangular pyramid, the volume of the pyramid becomes quadrupled.