Rural Hungary

Somewhat embarrassed to be asking this here but hopefully one of you can help!
I know the answer but need to be able to show how to get there.

A cone and cylinder have the same volume. Cone - diameter = d height = y Cylinder - diameter = y length = x find the ratio x:y

Son began,
1/3(pidy) = piyx
pidy = 3piyx
dy = 3yx
d = 3x
x = d/3

how do we get to a ratio of 1:3 ??

Hope somebody can help!

FenTiger

Not a problem .....
This website will tell you.
http://www.mathwarehouse.com/solid-g...me-of-cone.php

fidobsa

Not sure about the workings you have shown. Is he saying that because both cone and volume formulae are multiples of y you can cancel the squaring operation in the pi r squared part? These things are difficult to show on a computer as you can't type exponents or crossings out.

FenTiger

If my knowledge is correct the "1/3" figure has been proved to be the dividing factor to calculate the volume of a cone.

Rural Hungary

Error in original equation - my bad....

He now has,

pi (d/2)² = x pi (y/2)²
3

= (d/2)² = x (y/2)²
3

= (d/2)² = 3x(y/2)²

= if correct so far and he square roots, does the 3x become the square root of 3x

Rural Hungary

That's right, so the volume of the cone is the left side of the equation which equals the volume of the cylinder. Using the equation, he has to work out the ratio of x:y where x is the length of the cylinder and y the diameter. Time for me to

fidobsa

What's happened to y, the height of the cone?

Rural Hungary

It got fed up waiting and went off to do something better with it's time! Similar to the aforementioned son however, I shall persevere.

pi y (d/2)² = x pi (y/2)²
3

= y (d/2)² = x (y/2)²
3

= y (d/2)² = 3x(y/2)²

= square root then multiply by two? yd = 3xy
__________________

Rural Hungary

Beginning to think this is a badly written question

If it stated the diameters and heights were the same, then it would be

1/3 pi r² h= pi r² h and easy to work through however, it further confuses things but not making it clear which y it is referring to.

By not stating diameter & height are the same, surely this is beyond gcse level?

fidobsa

I was trying to do it by getting an expression for d on its own then substituting that for d in the original equation then dividing both sides by y then dividing both sides by x but I seemed to end up with 3x = 3y !

Rural Hungary

If making d the subject, I get sqrt 3x ( y), to then substitute that is more than I would expect them to ask at this level and well done you for trying.

I'll look at it again over the weekend as it shouldn't be this difficult

heli2010

did you get answer to this ?

3x=y or 3:1 is what I get

Rural Hungary

Hi there, I can't remember what we got but never did we get the answer that the book gave 1:3 and so we gave up and decided the book had given the wrong answer. It is honestly one of the worst maths books I have ever used, we have spent more time trying to rework (wrong answers) only to discover the answer in the book is wrong or that they have printed the right answers in the wrong order and so we have to try and work out which is which. A google search threw up a couple of complaints about mistakes in the answer book so we don't feel too bad - quadratic equations now then exam in four weeks

FenTiger

Fingers crossed the examiners have the right answers book!

heli2010

love quadratics which exam you doing ?