Volumes of Solids with Known Cross Section Project

[enn]

I'm trying to get started on this project but am totally confused about how to find the volume of the solid. All the information I was given was the following:

y= √x

boundaries: 0,9

cross sections: isosceles right triangle

how the hell do I get started?!

 

[Dick]

I'm trying to get started on this project but am totally confused about how to find the volume of the solid. All the information I was given was the following:

y= √x

boundaries: 0,9

cross sections: isosceles right triangle

how the hell do I get started?!

You use that the integral of area is equal to volume. You certainly need a little more information. My guess is that you are supposed to assume one of the sides of the triangle is between (x,0) and (x,sqrt(x)). Whether it's the hypotenuse of the triangle or the side is yours to guess unless they gave you a little more info.

 

[HallsofIvy]

I'm trying to get started on this project but am totally confused about how to find the volume of the solid. All the information I was given was the following:

y= √x

boundaries: 0,9

cross sections: isosceles right triangle

how the hell do I get started?!

You are doing just about everything wrong here. First, you are being rude- not a good way to ask for help. Second, I don't believe this was "all the information" you were given! For example, I'll bet you were told what "y= √x" means and you don't tell us that. I suspect you were told that the right angle of that "iososceles right triangle" lies on the the x-axis and another vertex on the graph of y= √x. Also, I'll bet that you were NOT told "boundaries: 0, 9" but were told that one end of the solid is at x= 0 and the other at x= 9.

If that is true then an isosceles right triangle with right angle on the x-axis and another vertex at y= √x has both legs of length √x and so area (1/2)bh= (1/2)(√x)(√x)= x/2. If we imagine one cross section "slab" as having thickness "dx" then its volume is (x/2)dx. Find the whole volume by integrating that.