# Thread: Volume around the Axis

1. ## Volume around the Axis

Hello there,

7. Find the volume of a solid whose base is the region perpindicular to the y axis betweeen the x axis and the curve $y=4-x^2$, and whose perpindicular cross sections are equilateral triangles with a side that lies on the base.

I'm really not sure what to do here. I can't find anything like this in our notes.
Thanks for any help.

2. Originally Posted by karisrou
Hello there,

7. Find the volume of a solid whose base is the region perpindicular to the y axis betweeen the x axis and the curve y=4 - x $y=4-x^2$, and whose perpindicular cross sections are equilateral triangles with a side that lies on the base.

I'm really not sure what to do here. I can't find anything like this in our notes.
Thanks for any help.
your problem statement is disjointed and confusing ... is that the exact wording as you read it?

3. Yeah, thats exactly as it appeared on the paper

4. including the coordinate axes, please confirm that two functions are region boundaries ... the line $y = 4-x$ and the curve $y = 4-x^2$

5. its just $4-x^2$

sorry, messed that up

6. area of an equilateral triangle with side length "s" is

$A = \frac{\sqrt{3}}{4} s^2$

side length for each cross-section is the horizontal distance from the y-axis to the curve
$y = 4-x^2$.

using the curve's equation, solve for the horizontal distance $x$ and use that expression in terms of $y$ to set up an integral in the form $V = \int_c^d A(y) \, dy$