a right circular cylinder, radius of base x,height y, is inscribed in a right circular cone,radius of base r and height h. express y as function of x (r and h are constants)

- anonymous

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- goformit100

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- goformit100

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- goformit100

@hartnn Help am I correct ?

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## More answers

- hartnn

where's the cone ?

- goformit100

read cylinder in the question

- goformit100

oops

- goformit100

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- hartnn

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- goformit100

OOps I am sorry again

- goformit100

Sorry @nhorzkie

- anonymous

its ok

- dan815

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- dan815

similar triangles

- dan815

if u cut a plane right in the middle and examine this cross section

- dan815

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- dan815

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- dan815

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- dan815

now all you need to do is write Y as a function of x

- dan815

sorry this is is wrong division

- dan815

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- dan815

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- anonymous

thanks :)

- dan815

thhankks :D

- dan815

use open study more ill cya later

- dan815

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- dan815

can u see that no matter what the shape that will show up on that plane is always a Triangle and a square in the middle

- dan815

say i rotate that plane around the z* axis

- dan815

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- dan815

so what we want to do is, look at that eye level shape you see only

- dan815

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- dan815

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- dan815

then u will see a square

- dan815

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- anonymous

haha yah, cute little person.

- dan815

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- dan815

if the person was standing on the x axis he will see this

- dan815

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- dan815

similariliy he will see the cone as a triangle

- dan815

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- dan815

but this doesnt hamper our relationship of the radius and height

- dan815

these are equal in dboth diagrams, except the radius of the circle just looks like the length of the square
and the hieght of the cone and cylinder is the hieght of square and triangle

- dan815

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- dan815

triangle ABC is similar to EDC
because they have equal angles

- dan815

a 90 degree angle angle C which is common in both triangles and obviously that means 180-c-90 = same angle for A and E

- dan815

now that we have proven these are also similar triangles we can write the proportion of the smaller triangle sides = the proportion of the bigger triangle sides

- dan815

if you are still following... all this then id be amazed.. its hard to teach on here, we can only really help u solve thing and help you see a little better but teaching concepts not that easy

- anonymous

yes im still following and your a big help now i understand! really thanks! :)

- dan815

okay then all thats left is to fill in the information you know and write that proportion equation

- dan815

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- dan815

okay so we know triangle ABC~ ECD so
CB/BA = CD/DE

- dan815

CB= R,BA=h,CD=R-x,DE=y
CB/BA=CD/DE becomes
R/h=(R-x)/y
solve for y
y=h(R-x)/R

- dan815

h and r are just some random constant so
now u have y = f(x)
some function of x

- anonymous

one more thing, whats the meaning of "r,h are constant?"

- dan815

they are not given.. they can be any number, given those numbers your cone and cylinder will look differently

- dan815

basically you solved the formula right now
so when they give you a value for r and h you can just plug it into the formula and you quickly know how y is changing as function of x

- anonymous

Done ! :) hopefully next time i post. you're online thanks.

- dan815

u dont need me to solve lol

- anonymous

hahaha ok I continue my homework. Godbless.

- dan815

u 2!

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