# A level Maths

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Figure 2 shows a hollow cone with radius R and vertical height H and a cylinder with radius r and height h . The cone sits on top of the cylinder so that their bases are level and the top of the cylinder is in contact with the inside of the cone as shown. The ratio of the heights hH is equal to p .

Express the ratio of the radii rR in terms of p .

I would appreciate any hints.

Last edited by Sahba7413; 8 months ago

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#2

Drop a height line down from the top of the cone to the base of a cylinder, and a radius R out from the bottom of this line.

You then have a pair of similar triangles to work with.

You then have a pair of similar triangles to work with.

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(Original post by

Drop a height line down from the top of the cone to the base of a cylinder, and a radius R out from the bottom of this line.

You then have a pair of similar triangles to work with.

**dextrous63**)Drop a height line down from the top of the cone to the base of a cylinder, and a radius R out from the bottom of this line.

You then have a pair of similar triangles to work with.

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#4

(Original post by

So would rR euqal to p as well, as hH is equal to P. Due to the fact that they are similar triangles.

**Sahba7413**)So would rR euqal to p as well, as hH is equal to P. Due to the fact that they are similar triangles.

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(Original post by

Not quite. What is the height of the smaller triangle?

**dextrous63**)Not quite. What is the height of the smaller triangle?

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#6

(Original post by

I'm not really sure, would it be H-h?

**Sahba7413**)I'm not really sure, would it be H-h?

You know that h/H = p

You also know that (from the similarity of the triangles) (H-h)/r = H/R.

You can rearrange this to find r/R

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(Original post by

Yes.

You know that h/H = p

You also know that (from the similarity of the triangles) (H-h)/r = H/R.

You can rearrange this to find r/R

**dextrous63**)Yes.

You know that h/H = p

You also know that (from the similarity of the triangles) (H-h)/r = H/R.

You can rearrange this to find r/R

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#8

Would someone mind explaining this further? I understand about the similar triangles, but how do I go from knowing that (H-h)/r = H/R and the fact that h/H is p to finding out r/R, I am confused about how to take the next step to rearrange

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#9

(Original post by

Would someone mind explaining this further? I understand about the similar triangles, but how do I go from knowing that (H-h)/r = H/R and the fact that h/H is p to finding out r/R, I am confused about how to take the next step to rearrange

**jasmine_GCSE**)Would someone mind explaining this further? I understand about the similar triangles, but how do I go from knowing that (H-h)/r = H/R and the fact that h/H is p to finding out r/R, I am confused about how to take the next step to rearrange

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#10

(Original post by

You're replying to a 7-month old thread but first of all can you rearrange (H-h)/r = H/R to get r/R on one side?

**davros**)You're replying to a 7-month old thread but first of all can you rearrange (H-h)/r = H/R to get r/R on one side?

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#11

(Original post by

Hahahah sorry I realised it was old but I think they must have been doing the same maths course as I am now! I couldn't get r/R for some reason, I think I'm over complicating it ://///

**jasmine_GCSE**)Hahahah sorry I realised it was old but I think they must have been doing the same maths course as I am now! I couldn't get r/R for some reason, I think I'm over complicating it ://///

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#12

(Original post by

That's OK - have you got it now?

**davros**)That's OK - have you got it now?

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#13

(Original post by

nope haha I can't work it out

**jasmine_GCSE**)nope haha I can't work it out

What can you do first to get r onto the RHS?

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#15

(Original post by

Multiply by r so Hr/R, How do I get rid of the H though ?

**jasmine_GCSE**)Multiply by r so Hr/R, How do I get rid of the H though ?

Divide both sides by H and what do you get?

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#18

(Original post by

oh actually, r/R=1-h

**jasmine_GCSE**)oh actually, r/R=1-h

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#19

Sorry to ask, I understood all of the rearranging of this formula to make r/R the subject of the formula, but I am very confused about how you got the formula in the first place. How did you know (H-h)/r = H/R ? What law of similar shapes do I have to know to arrive at this equation here?

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#20

(Original post by

Sorry to ask, I understood all of the rearranging of this formula to make r/R the subject of the formula, but I am very confused about how you got the formula in the first place. How did you know (H-h)/r = H/R ? What law of similar shapes do I have to know to arrive at this equation here?

**ila.1**)Sorry to ask, I understood all of the rearranging of this formula to make r/R the subject of the formula, but I am very confused about how you got the formula in the first place. How did you know (H-h)/r = H/R ? What law of similar shapes do I have to know to arrive at this equation here?

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