Wording question

1. Jan 30, 2008

kplooksafterme

1. The problem statement, all variables and given/known data
Consider the solid S described below.
The base of S is the region enclosed by the parabola y = 5 - 2x2 and the x-axis. Cross-sections perpendicular to the y-axis are squares.
Find the volume V of this solid.

2. Relevant equations

3. The attempt at a solution
I know how to answer these types of questions, but my question is what exactly does the question ask for? I can find the area bound by the parabola and the x-axis, but what does "cross-sections perpendicular to the y-axis are squares" mean?
thanks for any help

2. Jan 30, 2008

NateTG

If the bounding functions were, for example, $y=x+1$, $y=-x+1$ and [tex]y=0[/itex] then the solid would be a square pyramid.

The object that's being described is something like a sqare 'bubble pyramid'.

3. Jan 30, 2008

HallsofIvy

Staff Emeritus
Imagine squares made of foam. at the base of the parabola, since y= 5- 2x2 has x-intercepts at $\pm\sqrt{5/2}$ your square have height as well as base of length $2\sqrt{5/2}$ (and so area 10). As y increases the corresponding x values decrease and so does the height of the square. Your solid is bounded by 4 curved sides. Of course, there is the base which is that parabola itself. There will also be two "edges" arcing from (-1, 0, $-\sqrt{5/2}$) down to (0, 5, 0) and from (1, 0, [itex]\sqrt{5/2}[itex]) down to (0, 5, 0).