# Solution to #1-4

Paper 1 Difficulty: Medium

The volume of a pyramid with base length l, base width w, and height h is given by $V=\frac{lwh}{3}$. The volume of the pyramid was measured with an uncertainty of 12%, while the base length and base width were measured with an uncertainty of 4%. What is the uncertainty of the height of the pyramid?
A) 2%
B) 3%
C) 4%
D) 6%

[Maximum mark: 1]

$\frac{\Delta V}{V}=0.12\\ \frac{\Delta l}{l}=\frac{\Delta w}{w}=0.04\\ V=\frac{lwh}{3}\rightarrow \frac{\Delta V}{V}=\frac{\Delta l}{l}+\frac{\Delta w}{w}+\frac{\Delta h}{h}\\ \frac{\Delta h}{h}=\frac{\Delta V}{V}-\frac{\Delta l}{l}-\frac{\Delta w}{w}\\ \frac{\Delta h}{h}=0.12-0.04-0.04=0.04\\ 0.04\times 100 =4\%$