Optimization

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

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.

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.

Thanks. Doesn’t surprise me, this book is full of errors. Really appreciate that.

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.