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# Optimization watch

1. 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.
2. 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.
3. (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
4. (Original post by Shaanv)
See above
Hi. That is how I have tackled it. I have attached the question and my working so far for you to look at. Thanks
Attached Images

5. (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.
6. (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.
7. (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.
8. (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.
Thanks. Doesn’t surprise me, this book is full of errors. Really appreciate that.
9. (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?
10. (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.
11. (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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