How much oxygen absorbing area does an insect have?

[salmayoussef]

Homework Statement

Insects don't need lungs. They breath through their skins. In this way they can get enough oxygen to fuel the basic metabolism that is common to all life. Approximate an insect by a cylinder of diameter 4mm and length 5mm. Assuming that the density of the insect is approximately that of water (i.e. 1.0 gram per cubic centimeter), how much oxygen absorbing area, in square meters, does the insect have for each kilogram of body mass?

I did my best to understand what this question is asking me and tried to solve it to no avail.

I know:

density = 1 g/cm³
diameter = 4 mm = 0.004 m
length = 5 mm = 0.005 m

Homework Equations

SA of a cylinder
Volume of a cylinder

The Attempt at a Solution

I tried to solve for the SA of the cylinder

SA = 2∏rh + 2∏r²
SA = 2∏(0.002)(0.005) + 2∏(0.002)²
SA = 0.000087964 m²

Then I tried to solve for volume

V = ∏r²h
V = ∏(0.002)²h
V = 0.005012566 m³

Then I tried to find "oxygen absorbing area" in m² for each kg of body fat

0.000087964 m²/0.0005012 kg = 0.1755

Unfortunately it isn't the right answer! Can anybody point out what I've been doing wrong? Thanks! :shy:

 

[happysmiles36]

Your equations and math formulas look good. However, you are given density in 1 g/cm³. The question asks for it in kg. Your main error I notice right off the bat is you are assuming volume = mass which is incorrect

So here is what I would do.

Convert units!

Diameter: 4mm
Height (length): 5mm
Density: 1g/cm³

Because density is in cm, I suggest changing mm to cm not to m until the end so its easier. You also need to convert g to kg. Post what you have and I'll explain the rest!

 

[salmayoussef]

Your main error I notice right off the bat is you are assuming volume = mass which is incorrect

But if the ratio is 1:1, wouldn't that mean that 0.5012 cm³ is 0.5012 g?

 

[happysmiles36]

I will explain that, just convert the units for now, trust me, will be easier to follow.

Impatient answer:
(Mass=volumexdensity)

 

[salmayoussef]

Okay, okay, so:

diameter = 4 mm = 0.4 cm
length (height) = 5 mm = 0.5 cm
density = 1 g/cm³ OR 1000 kg/m³

Using these units, SA = 0.879645 cm² and v = 0.06283 cm³.

Correct?

 

[happysmiles36]

Correct.
So the question wants the amount of SA/Mass

You already have SA so that is done (just need to convert to m^2[/10000]), however to get mass you multiply density and volume.
density should be 0.001 kg/cm^3.
Note your volume is in cm^3. converting cm^3 to m^3 is just extra work.

You get the correct answer with this.

 

[salmayoussef]

I got 1.40 which is the correct answer! Thank you so much! :thumbs:

 

[happysmiles36]

Your welcome :D