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A diagram shows a solid cylinder. The cylinder has radius 4√3 cm and height h cm. The total surface area of the cylinder is 56√6 cm2 . Find the exact value of h. Give your answer in the form a√ 2 + b√ 3, where a and b are integers. Show your working clearly. (5 marks)
2. I'm not sure what to do exactly but I'm guessing it's something to do with surds?
3. yeah it is something to do with surds but i dont know how to work it out using it
4. (Original post by Taahira_)

A diagram shows a solid cylinder. The cylinder has radius 4√3 cm and height h cm. The total surface area of the cylinder is 56√6 cm2 . Find the exact value of h. Give your answer in the form a√ 2 + b√ 3, where a and b are integers. Show your working clearly. (5 marks)
Post it in Maths
5. I found h was 2.2852653329. Substituting it into the formula to calculate the SA of a cylinder looks like it is h. However, I have no idea how to put it into that form....
6. Try to find a formula for "total surface area" in terms of r and h and let this be equal to 56√6. Sub in the specific value of r as given (4√3) but leave h as is (you don't yet know it). Rearrange for h.

Does this make any sense? Give it a try and see where you get
7. (Original post by Bapujisamji)
Thanks and the question says its 56π√6 :I
8. (Original post by President Snow)
Try to find a formula for "total surface area" in terms of r and h and let this be equal to 56√6. Sub in the specific value of r as given (4√3) but leave h as is (you don't yet know it). Rearrange for h.

Does this make any sense? Give it a try and see where you get
I tried but i got stuck in the middle, it was too confusing
9. (Original post by Taahira_)
I tried but i got stuck in the middle, it was too confusing
What formula are you using for the total surface area? If you upload a scan of your work so far I'll try to give some hints on how to carry on thinking about the problem. If there's a lot of crossing out it may be a good idea to write out all of the good steps you have taken so far on a new sheet of paper nice and neatly.

I'm currently studying for a maths degree - a lot of what I do every day is tackling very difficult maths problems and this involves lots of trial and error on paper. But, when things start getting very confusing, it sometimes helps to clear the mind, focus on the good lines so far, and write them out neatly on a new sheet of paper to make everything clearer.

This is a difficult problem - it's supposed to be difficult. But if you keep fighting it - and I'll try to help you get there, it will slowly get easier and you'll learn something from it. That's the aim of revision. Stick in there
10. (Original post by President Snow)
What formula are you using for the total surface area? If you upload a scan of your work so far I'll try to give some hints on how to carry on thinking about the problem. If there's a lot of crossing out it may be a good idea to write out all of the good steps you have taken so far on a new sheet of paper nice and neatly.

I'm currently studying for a maths degree - a lot of what I do every day is tackling very difficult maths problems and this involves lots of trial and error on paper. But, when things start getting very confusing, it sometimes helps to clear the mind, focus on the good lines so far, and write them out neatly on a new sheet of paper to make everything clearer.

This is a difficult problem - it's supposed to be difficult. But if you keep fighting it - and I'll try to help you get there, it will slowly get easier and you'll learn something from it. That's the aim of revision. Stick in there
Okay so here's what I done... I didn't use a formula because I didn't know what it was - I just found the area of the 2 circles and the area of the rectangle part of the cylinder (if that makes sense) and I added the two together and then I rearranged to get h the subject and yeah...that's where I am stuck. I don't think what I did was right though
11. (Original post by Taahira_)

A diagram shows a solid cylinder. The cylinder has radius 4√3 cm and height h cm. The total surface area of the cylinder is 56√6 cm2 . Find the exact value of h. Give your answer in the form a√ 2 + b√ 3, where a and b are integers. Show your working clearly. (5 marks)
Total surface area = 2pi*r*(r+h), so 2pi*4root3*(4root3+h)=56root6 -> 8pi*root3*(4root3+h)=56root6.
Thus 4root3+h=7root2/pi -> h = 7/pi*root2-4root3, so the question is wrong.
12. (Original post by Taahira_)
Thanks and the question says its 56π√6 :I
No worries. If you can give me some rep that would be much appreciated.
13. (Original post by Taahira_)
Okay so here's what I done... I didn't use a formula because I didn't know what it was - I just found the area of the 2 circles and the area of the rectangle part of the cylinder (if that makes sense) and I added the two together and then I rearranged to get h the subject and yeah...that's where I am stuck. I don't think what I did was right though
That's a really good start! Now, the sqrt(3) on the bottom of the fraction is inconvenient and unwanted. We need to get rid of it.

To do this we use a process called "rationalising the denominator" (getting rid of square roots and the like on the bottom of the fraction).

To do this, times both the top and the bottom of the fraction by sqrt(3). Note also that sqrt(6)=sqrt(3)*sqrt(2) and that sqrt(3)*sqrt(3)=sqrt(3)^2 = 3.

Can you see how to carry on from here?

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