Cylindrical pieces of wood are to be shipped to a furniture production facility. Additional shipping costs are applied to any piece of wood that weighs more than 1400 lbs. The densities for the pieces of wood being shipped are shown below:

Which of the following pieces of wood would incur additional shipping costs? Select all that apply.

A. Elm log

radius = 2ft

height = 2ft

B. Aspen log

radius = 3ft

height = 2ft

C. Black Ash log

radius = 2ft

height = 3ft

D. Pecan log

radius = 3ft

height = 1ft

E. Cuban Mahogany log

radius = 4ft

height = 1ft

macabresubwoofer Apr 4, 2019

#1**0 **

Calculate the volume of the logs: pi r^2 h (ft^3) then multiply by the densities ( lbs/ft^3) you are given to find the weight (lbs) of each of the logs to see which is overweight (>1400 lbs).... Try it!

ElectricPavlov Apr 4, 2019

#3**0 **

Let's see:

Volume of pecan log pi r^2 h = pi 3^2 (1) = 28.27 ft^3

weight of pecan log Volume x density = 28.27 ft^3 x 47 lbs/ft^3 = 1357.2 lbs Nope...it is not 'D'...try again!

ElectricPavlov
Apr 4, 2019

#7**0 **

Mass = volume * density = pi * (radius)^2 (height) (density )

A. pi * (2)^2 (2) ( 50) ≈ 1257 no

B. pi * ( 3)^2 ( 2) ( 26) ≈ 1470 yes

C . pi * ( 2)^2 ( 3) ( 33) ≈ 1244 no

D. pi * ( 3)^2 ( 1) * (47) ≈ 1329 no

E. pi * ( 4)^2 ( 1) ( 40) ≈ 2011 yes

"B" and "E" will incur additional shipping costs

CPhill Apr 4, 2019

#8**+1 **

Thanks a lot on that one

How about this one,

A new company is starting up and they are creating care packages to be sent to children in high poverty areas. All of the items for the package need to fit inside of one container that does not have a lid. The company has a great team that is designing a container that has a total volume of 2.5 ft^3. For the shape, they are deciding between a rectangular prism with a base dimension of 1 ft x 2 ft and a cylinder with a base area of 2.5 ft^2. The material they have selected to make the packages cost $1.30 per square foot. Which package design will cost the company less to create and by approximately how much? Use π = 3.14

macabresubwoofer
Apr 4, 2019