# Finding line intersection..

#### shamieh

##### Active member
Question: Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

$$\displaystyle x = 2\sqrt{y}, x = 0, y = 9$$

So I know what the graph looks like. But how do i find the points of intersection? wouldn't i just set them equal to eachother? so like $$\displaystyle 2\sqrt{y} = 9$$ and solve? but how do I solve this equation properly?

#### ZaidAlyafey

##### Well-known member
MHB Math Helper
Question: Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

$$\displaystyle x = 2\sqrt{y}, x = 0, y = 9$$

So I know what the graph looks like. But how do i find the points of intersection? wouldn't i just set them equal to eachother? so like $$\displaystyle 2\sqrt{y} = 9$$ and solve? but how do I solve this equation properly?
You have the equation $$\displaystyle x=2\sqrt{y}$$ and you have the equation $x=0$. Just plug the value of $x=0$ in the equation of the curve. So we have $2\sqrt{y}=0$ and hence by squaring we have $4y=0$ or $y=0$. Hence the curve $x=2\sqrt{y}$ intersects the y-axis at the point $(0,0)$. Similariy find the point of intersection of the two cruves $x=2\sqrt{y}$ and $y=9$.

#### shamieh

##### Active member
oh i see! Thanks! so then by setting y = 0 I get 9, then i plug in 9 back to the function and get 2*3 =6, so it intersects at (6,9) ?

#### ZaidAlyafey

##### Well-known member
MHB Math Helper
oh i see! Thanks! so then by setting y = 0 I get 9
Why setting the value of $y=0$ ?

, then i plug in 9 back to the function and get 2*3 =6, so it intersects at (6,9) ?
Correct !

#### Prove It

##### Well-known member
MHB Math Helper
Question: Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. Sketch the region, the solid, and a typical disk or washer.

$$\displaystyle x = 2\sqrt{y}, x = 0, y = 9$$

So I know what the graph looks like. But how do i find the points of intersection? wouldn't i just set them equal to eachother? so like $$\displaystyle 2\sqrt{y} = 9$$ and solve? but how do I solve this equation properly?
When doing any area or volume of region questions, the first step should ALWAYS be to do a sketch of the region. Then you can at least get an idea of where the intersections are and this can give you an idea on how to refine them.