Question

The question that goes to this imagine What is the density if the pine log? Show your work. Need help with this homework question so I do good on my test

Answer 1

The density of an object is given by its mass (or its weight in this case) divided by its volume. So in order to find the density of the pine log we first need to find its volume. A log is basically a cylinder so it has a circular base and a certain height. We are told that the radius of the base is 5 in long and its height is its length: 30 in. The area of its circular base is given by:

$A=\pi r^2=\pi\cdot(5)^2=25\pi$

Then if we multiply the area by the height we find the volume:

$V=25\pi\cdot30=750\pi$

So the volume of the log is 750π in³. Now that we have its volume we can find its density:

$d=\frac{\text{weight}}{\text{volume}}=\frac{42.63\text{ lbs}^{}}{750\pi in^3}=\frac{0.05684}{\pi}\text{ }\frac{\text{lbs}}{in^3}$

And that's the density of the log 0.05684/π lbs/in³.