Question

PLEASE HELP TIMED ASSIGNMENT PLATOwhat is the density of the oak board that is 5.5 inches wide, 1.5 inches thick and 3 feet long. show your work.Weight: 8.05 lbs

Answer 1

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.

`V=w\cdot l\cdot t=5.5in\cdot(3ft\cdot(12in)/(1ft))\cdot1.5in=297\text{ cubic inches}`

Then, if we divide the weight by the volume, we get:

`\rho=(W)/(V)=\frac{8.05\text{ lbs}}{297\text{ in}^3}\approx0.027\frac{\text{ lbs}}{\text{ in}^3}`

If we express the density in pounds per cubic feet, we can write:

`\rho=(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}`

Answer: the density is 46.84 pounds per cubic feet.