I saw this question on Florida state geometry test. Few of my students got it right.
In the question, the students were given the inner and outer diameter of the pipe as well as its mass and length. Like this:
Find the mass of a 50 cm long pipe with an inner diameter of 2 cm and an outer diameter of 3 cm. The density of the metal in the pipe is 7 g/cm^3.
Take a few minutes to work this out on your own. Draw a picture. Hint: The volume of the pipe is the same as the volume of one cylinder minus the volume of another cylinder. Let's call the volume of the big cylinder V and the volume of the little cylinder v.
If we calculate the volume of a cylinder whose diameter is the same as the outer diameter of the pipe and then subtract the volume of a cylinder whose diameter is the same as the inner diameter of the pipe, we get the volume of the pipe itself. The formula for the volume of a cylinder is V= pi*(R^2)*h. We need to remember that a radius is half a diameter.
V - v = pi*((3/2)^2)*50 - pi*((2/2)^2)*50
V - v = pi*50*((3/2)^2 - (1)^2)) = 196.349 cm^3
Since density is mass divided by volume, multiplying volume with density gives us mass.
(196.349 cm^3)*(7 g/cm^3) = 1374 g
Everything is easy when you know what to do. I was in engineering school the first time I saw a problem like this.
No comments:
Post a Comment