sketch of a solid for calculating volume using slicing method

Question

In reference to the textbook: Thomas’ Calculus, 14th edition, Heil, Weir & Hass

In chapter 6, section 1, Exercise 1: We need to find the volume of a solid using the slicing method

It says that the solid lies between planes perpendicular to the x-axis at x $=$ $0$ and x $=$ $4$. The cross-sections perpendicular to the axis on the interval $0 \leq x \leq 4$ are squares whose diagonals run from the parabola $y = -\sqrt{x}$ to the parabola $y = +\sqrt{x}$ .

I would like to note that I have the solution available from my professor, but my problem lies in visualizing and sketching the solid. Can you please help me in sketching the solid on the coordinate system?

I understand the sketching of the perpendicular planes, and I get the idea that the cross-sections take the shape of a square, and so the edges of their diagonals go from $y = -\sqrt{x}$ to $y = +\sqrt{x}$. But how does the final shape of its volume look like??

Can you at least provide me with hints of the sketch so it would help me in further exercises? Thank you.

Answer 1

($x$ axis is the axis of the volume, $y$ axis on the right, $z$ axis vertical)

For a very similar problem see here.

Matlab program:

clear all;close all; hold on;box on
plot3([0,4,0,0,0,0],[0,0,0,2,0,0],[0,0,0,0,0,2],'k');%axes
view([143,10]);% azimuth and elevation angle for observer's view
for x=0:0.1:4;% a square per value of x
   s=sqrt(x);
   X=[x,x,x,x,x];Y=[s,0,-s,0,s];Z=[0,s,0,-s,0]; coord. of squares' vertices
   plot3(X,Y,Z);
end;