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Thread: How do I calculate these surface areas?

  1. #1 How do I calculate these surface areas? 
    j.r
    j.r is offline
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    Hello,

    I'd be very grateful if anyone might help me out. I'm a new student to Biology and have a lot of trouble when it comes to math. I've been studying 'surface area to volume ratio' and have just undertaken the following related exercise:



    I apologise if the screen-shot image of the exercise isn't appearing in my post. I'm having trouble getting the URL to work for the forum. You should be able to see it by following the link:

    http://i1088.photobucket.com/albums/...olumeratio.jpg

    As you can see, the exercise involves filling in gaps with answers to a number of questions. I had to select the number I thought to be the correct answer to each question by clicking on each of the grey arrows/triangles and selecting an answer from a drop down list of multiple choice options. The image I have posted here is a screen-shot of the exercise with all the correct answers revealed by the computer.

    I was able to work through this exercise successfully myself up until the part that I've drawn a red box around. Unfortunately I have no idea how find the answer "9.42 micrometers^2" to the question "The surface area of the cylinder (minus the area of the two circular ends) is..."
    Nor, in turn, do I know how to find the correct answer "12.6 micrometers^2" to the question "The total surface area is..."

    I'd really appreciate if anyone could please explain to me how I must go about correctly calculating the surface area of the cylinder (minus the area of the two circular ends) and then the total surface area. What equations must I do to get to these two answers?

    I know that to calculate the surface area of a cylinder the equation is: (2*pi*r^2*height) + 2*pi*r^2

    However, when I try to find the answer to the question "The surface area of the cylinder (minus the area of the two circular ends) is..." using the surface area of a cylinder equation, I don't get an answer anywhere near 9.42 micrometers^2, but something a great deal lower. The "(minus the area of the two circular ends)" part is something I really don't understand at all either. What must I do there?
    My answer, in the first stage, using the equation (2*pi*r^2*height) + 2*pi*r^2 (without even worrying about subtracting the area of the two circular ends) already came to something far below 9.42 micrometers^2. It won't be possible for me to bring the answer up to the figure 9.42^2 by subtracting the area of the two circular ends. It will in fact only make my answer even smaller and further in the opposite direction of 9.42^2.
    I'm very confused about how to approach any part of these two questions. Could anyone possibly explain to me what I must do/what steps I must take (and why) to work through these two questions to reach the answers 9.42 micrometres^2 and 12.6 micrometres^2?

    Thank you very much!


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  3. #2  
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    Hi! What you want to do is use 2*pi*r*h for the cylinder part of the question, you don't include the other part because it asked you to exclude the ends.
    Then! For the total surface area you use the surface area of the ends treating them as a sphere :-D (4*pi*r^2)


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  4. #3 Re: How do I calculate these surface areas? 
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    Quote Originally Posted by j.r
    I was able to work through this exercise successfully myself up until the part that I've drawn a red box around. Unfortunately I have no idea how find the answer "9.42 micrometers^2" to the question "The surface area of the cylinder (minus the area of the two circular ends) is..."
    It won't be possible for me to bring the answer up to the figure 9.42^2 by subtracting the area of the two circular ends. It will in fact only make my answer even smaller and further in the opposite direction of 9.42^2.
    No, you are mistaken. The answer is not 9.42 squared, it's 9.42, and the units are square micrometers. That's what the "micrometers^2" indicates.
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