Respuesta :
The density is equal to the quotient between the weight and the volume of the board.
We can calculate the volume of the board as the volume of a rectangular prism: width by length by thickness.
[tex]V=w\cdot l\cdot t=5.5in\cdot(3ft\cdot\frac{12in}{1ft})\cdot1.5in=297\text{ cubic inches}[/tex]Then, if we divide the weight by the volume, we get:
[tex]\rho=\frac{W}{V}=\frac{8.05\text{ lbs}}{297\text{ in}^3}\approx0.027\frac{\text{ lbs}}{\text{ in}^3}[/tex]If we express the density in pounds per cubic feet, we can write:
[tex]\rho=\frac{W}{V}=\frac{8.05\text{ lbs}}{297\text{ in}^3}\cdot(\frac{12\text{ in}}{1\text{ ft}})^3=\frac{8.05\text{ lbs}}{297\text{ in}^3}\cdot\frac{1728\text{ in}^3}{1\text{ ft}^3}\approx46.84\frac{\text{ lbs}}{\text{ ft}^3}[/tex]Answer: the density is 46.84 pounds per cubic feet.
