# Calculate the Volume of a Lemonsqueezer

## Homework Statement

$f(x)=\frac{1}{81}*x^4-\frac{5}{9}*x^2+4$
The tangent in Point P(6|0) when rotated around the y-Axis gives the Shape of the Squeezer. The bottom is at y=-5, the top at y=0

## The Attempt at a Solution

First I calculated the tangent and got

$t: y=4x-24$
Then I converted that to $x^2$ since I need that for the rotation around the y-Axis
$x^2=\frac{y^2}{16}+3y+36$

Then I rotated it:

$V=\pi\int\frac{y^2}{16}+3y+36dy = \pi(\frac{y^3}{48}+\frac{3y^2}{2}+36y)(0 to -5)$
$= \pi(0+0-(-\frac{125}{48}+\frac{75}{2}-180) = \pi(\frac{125}{48}-\frac{1800}{48}+\frac{8640}{48})$
$= \frac{6965\pi}{48} = 455.86$

Since this is in cL, which would equal around 4.6L I find the result a bit excessive. Have I made a mistake somewhere? Can someone please check for me? Thank you in advance :)

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LCKurtz
Homework Helper
Gold Member

## Homework Statement

$f(x)=\frac{1}{81}*x^4-\frac{5}{9}*x^2+4$
The tangent in Point P(6|0) when rotated around the y-Axis gives the Shape of the Squeezer. The bottom is at y=-5, the top at y=0

## The Attempt at a Solution

First I calculated the tangent and got

$t: y=4x-24$
Then I converted that to $x^2$ since I need that for the rotation around the y-Axis
$x^2=\frac{y^2}{16}+3y+36$

Then I rotated it:

$V=\pi\int\frac{y^2}{16}+3y+36dy = \pi(\frac{y^3}{48}+\frac{3y^2}{2}+36y)(0 to -5)$
$= \pi(0+0-(-\frac{125}{48}+\frac{75}{2}-180) = \pi(\frac{125}{48}-\frac{1800}{48}+\frac{8640}{48})$
$= \frac{6965\pi}{48} = 455.86$

Since this is in cL, which would equal around 4.6L I find the result a bit excessive. Have I made a mistake somewhere? Can someone please check for me? Thank you in advance :)

No mistake. That is correct.

Last edited by a moderator:
1 person
4.6L Lemonsqueezer? Okay thank you^^

LCKurtz
Homework Helper
Gold Member
4.6L Lemonsqueezer? Okay thank you^^

The problem states nothing about units. You can tell the 455.8 is reasonably close since the volume would be a bit less than a disk of radius ##6## and thickness ##5##$$5\pi 6^2 = 565.48$$

1 person
Yeah it does. It states 1 unit = 1cm and the Volume in cl
Thank you though :)