A square pyramid P has base with side $x$ m, height $y$ m and a volume of 300 m^3. Find

1. Use the volume scale factor for similar pyramids

For similar pyramids, if the height is doubled, the linear scale factor is $2$.

Volume scale factor $=2^3=8$.

New volume $=300\times 8=2400\text{ m}^3$.

1. Write the original volume in terms of $x$ and $y$

For pyramid P,
$\frac{1}{3}x^2y=300.$

2. Find the volume after changing the side and height

New volume
$=\frac{1}{3}(3x)^2\left(\frac{2}{3}y\right)$
$=\frac{1}{3}\cdot 9x^2\cdot \frac{2}{3}y$
$=6\left(\frac{1}{3}x^2y\right)$
$=6(300)=1800.$