Question

A blacksmith heated a metal whose cubic expansivity is 6.3×10^-6K^-1.The area expansivity is?

Answer 1

ANSWER

4.2 X 10⁻⁶ K⁻¹

EXPLANATION

The three common expansivities we usually have are linear, area and cubic:

$\begin{gathered} \text{linear }=\alpha \\ \text{ area }\beta=2\alpha \\ \text{ cubic }\gamma=3\alpha \end{gathered}$

If we have to cubic expansivity, we can find the linear by dividing by 3:

$\alpha=\frac{\gamma}{3}=\frac{6.3\times10^{-6}}{3}=2.1\times10^{-6}$

And then find the area expansivity by multiplying by 2:

$\beta=2\alpha=2\cdot2.1\times10^{-6}=4.2\times10^{-6}$