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    I am having trouble with an optimization question. I am presented with a medicine capsule made up of a cylinder with a hemisphere at either end. Volume = 0.6cm^3. I have to show that total surface area = 6/5r + 4/3pir^2. I can get the first part of 6/5r. But cannot see where the 4/3pir^2 comes from. I just end up with 6/5r + 4pir^2. Any help would be appreciated greatly.
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    How have u tackled the problem? Can u attach working out?

    First thing i would do is find an expression for volume then rearrange for the height, then substitute this into the equation for surface area.
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    (Original post by Mortifiedpenguin)
    I am having trouble with an optimization question. I am presented with a medicine capsule made up of a cylinder with a hemisphere at either end. Volume = 0.6cm^3. I have to show that total surface area = 6/5r + 4/3pir^2. I can get the first part of 6/5r. But cannot see where the 4/3pir^2 comes from. I just end up with 6/5r + 4pir^2. Any help would be appreciated greatly.
    See above
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    (Original post by Shaanv)
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    Hi. That is how I have tackled it. I have attached the question and my working so far for you to look at. Thanks
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    (Original post by Mortifiedpenguin)
    Hi. That is how I have tackled it. I have attached the question and my working so far for you to look at. Thanks
    When writing an expression for volume u neglected the two hemispheres, this led to a wrong answer.
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    (Original post by Shaanv)
    When writing an expression for volume u neglected the two hemispheres, this led to a wrong answer.
    But it only provides the volume of the cylinder not the hemispheres.
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    (Original post by Mortifiedpenguin)
    But it only provides the volume of the cylinder not the hemispheres.
    I can only think that it meant to say capsule not cylinder, as i approached the question as if the volume of the capsule was 0.6 and then i got the answer quoted in the book.
    Name:  01925734-D7CF-4C11-9B4E-E0AA8CF24A91.jpg.jpeg
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    (Original post by Shaanv)
    I can only think that it meant to say capsule not cylinder, as i approached the question as if the volume of the capsule was 0.6 and then i got the answer quoted in the book.
    Name:  01925734-D7CF-4C11-9B4E-E0AA8CF24A91.jpg.jpeg
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    Thanks. Doesn’t surprise me, this book is full of errors. Really appreciate that.
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    (Original post by Mortifiedpenguin)
    Thanks. Doesn’t surprise me, this book is full of errors. Really appreciate that.
    Not to worry.

    Which textbook are u using?
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    (Original post by Shaanv)
    Not to worry.

    Which textbook are u using?
    Leckie and Leckie cfe higher maths. There’s mistakes in a lot of the answers and mistakes in a lot of the questions themselves, it’s a pain. When you answer something and it’s wrong you start to question whether it’s the textbook or you.
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    (Original post by Mortifiedpenguin)
    Leckie and Leckie cfe higher maths. There’s mistakes in a lot of the answers and mistakes in a lot of the questions themselves, it’s a pain. When you answer something and it’s wrong you start to question whether it’s the textbook or you.
    Eventually u will have enough confidence to call the book wrong, i have found plenty of mistakes in the edexcel modular a level maths and further maths textbooks.

    U will be a better maths student for it.💪🏾👊🏾👌🏾
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