The diagram shows a right pyramid of height 45 cm. The volume of the liquid in the pyramid is half the volume of the pyramid. Calculate the depth, h cm, of the liquid. Answer ... cm

1. Set up the volume ratio using similarity

The liquid forms a smaller pyramid similar to the whole pyramid.

Since the volume of the liquid is half the volume of the pyramid,
$\left(\frac{h}{45}\right)^3=\frac{1}{2}$

2. Solve for the liquid depth

$\frac{h}{45}=\sqrt[3]{\frac{1}{2}}$

$h=45\sqrt[3]{\frac{1}{2}}$

$h=35.7\text{ cm} \quad \text{to 3 s.f.}$