the wood of a beech tree has a density of 46 pounds per cubic foot. a cylindrical log from a beech tree has…

the wood of a beech tree has a density of 46 pounds per cubic foot. a cylindrical log from a beech tree has a diameter of 2 feet and a height of 20 feet. what is the approximate weight, in pounds, of the log? round your answer to the nearest hundredth.

the wood of a beech tree has a density of 46 pounds per cubic foot. a cylindrical log from a beech tree has a diameter of 2 feet and a height of 20 feet. what is the approximate weight, in pounds, of the log? round your answer to the nearest hundredth.

Answer

Explanation:

Step1: Calculate the radius of the log

Given diameter $d = 2$ feet, radius $r=\frac{d}{2}=\frac{2}{2}=1$ foot.

Step2: Calculate the volume of the cylindrical log

The volume formula for a cylinder is $V=\pi r^{2}h$. Substitute $r = 1$ foot and $h = 20$ feet. So $V=\pi\times(1)^{2}\times20=20\pi$ cubic - feet.

Step3: Calculate the weight of the log

We know that density $\rho = 46$ pounds per cubic - foot. Weight $W=\rho\times V$. Substitute $\rho = 46$ and $V = 20\pi$. Then $W=46\times20\pi=920\pi\approx920\times3.14159 = 2880.2628\approx2880.26$ pounds.

Answer:

$2880.26$