## Volume of a solid

The base of a solid is the region bounded by the graphs of x=y^2 and x=4. "Each cross section is perpendicular to the x-axis is a triangle of altitude 2." Find the volume of the solid.

That was how it was worded, I'm guessing it meant Each cross section perpendicular to the x-axis is a triangle of altitude 2?

Assuming that's what it says. How are these problems tackled? The addition of the quoted sentence confuses me a tad bit on what direction to head.
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 So after looking at it some more, I got: Int{0 to 4} Sqrt(3)/4 * (4 - Sqrt(x))^2 dx ? Hrmm.. ok, I just noticed I didn't use the altitude...

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 "Each cross section is perpendicular to the x-axis is a triangle of altitude 2."
 I'm guessing it meant Each cross section perpendicular to the x-axis is a triangle of altitude 2?
Good guess! Did the problem really have that extraneous first "is"?

Since the area of a triangle is (1/2)h*b and h= 2, you only need to calculate b. The cross section is perpendicular to the x-axis so the base is the y distance. y, for specific x, ranges from x2 up to 4 so the distance is b= 4-x2. That is, the area of such a triangle is (1/2)(4-x2)(2)= 4- x2. Imagining each cross section as an infinitesmally this slab, of thickness dx (since the thickness, perpendicular to the plane, is in the x-direction), the "volume" of each slab is (4- x2)dx.

Putting all of the "slabs" together, the total volume is
$$\int_0^4(4-x^2)dx$$

I have absolutely no idea where you got all those square roots!

## Volume of a solid

shouldn't it be composed as a triple integral since you are dealing with a solid? or did I not read the problem correctly?
 this helped me a lot when I was in calc... making a graphical representation (even if it is 3 dimetions) can help a lot.

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