Need help with a Maths Question

Hi,

I need your help with a maths question that is really bugging me.

Here is the question:

The diagram below shows a pencil case. It is a cylinder with a length 12 cm and a radius of 5 cm.

(a) Calculate the volume of the pencil case. Give your answers correct to 2 decimal places.

(b) Show that a pencil, which is 14 cm long, can fit inside the pencil case.

I've done question (a) which is:

Pi r2 = Pi (5x5)
= 78.539

78.539 x 12 = 942.477
= 942.48

Then there is question (b), but I am unsure on how to figure it out with only having one information about the pencil, 14 cm length.

This is really important to me as I have a GCSE maths exam on monday and I am afraid that this may be one of the questions.

Thanks in advance
-Game677

I think it's a trick question...witch the answer would be cut it in two pieces

I'm not sure what kind of method you have to use, but I think that you would need to fit the pencil in it diagonally. In this case, you would need to use the Pythagorean Theorem.

What you'd have to do is cut the cylinder in half, using the rectangle, and just do the following:

c2 = a2 + b2
c2 = (2 x 5)2 + 12 2
c2 = 10 2 + 12 2
c2 = 100 + 144
c2 = 244
c = square root of 244
c = 15.62 cm

The pencil is 14 cm in length, so I assume it would fit.

Although I could be wrong, seeing as how the pencil case might be full, or just my idea was incorrect altogether.

If it's a serious question, then the way spartan said is the way to do it.

Though, I'm doing GCSE too, and I've never seen a question like that. If something similar does come up, just remember that method above.
Where did you find it, by the way?

Actually, using the "diagonal method" you have to consider the pencil's radius too (at least in the eraser side...)

but if it is less than 1 cm... it easily fits...

Originally Posted by Spartan-117

Pythagorean Theorem.

c2 = a2 + b2
c2 = (2 x 5)2 + 12 2
c2 = 10 2 + 12 2
c2 = 100 + 144
c2 = 244
c = square root of 244
c = 15.62 cm

The pencil is 14 cm in length, so I assume it would fit.

Thanks Spartan and everyone else for replying! Spartan was correct with the Pythagorean Theorem. And it helped me out with the Maths GCSEs, which I've done today and it was suprisingly easy. But I would just like to thank all of you for your replies.

Admins/Mods, you can lock this thread now!

-Game677

You all finished your exams now? I did mine this week I thought it went quite well, what about you?

I don't want to talk about exams xD....I did my maths exam yesterday....It was very very difficult.........I hate maths....

I'm in 6th grade so I don't have exams, but I go to a very hard priate school, I'm not sure if this is above my level but this year I can speak french/english and in maths we did substracting/add/multiply/divide fractions.

Whoa, what kind of math do you do?
I am in Eigth excel math. But I don't remember doing that before.

lol math.

Question answered. Take irrelevant discussion elsewhere, please.