Volume of the solid given cross sections... work shown.help!

[johnq2k7]

The base of a solid is the region bounded by y= 2*sqrt(sin(x)) and the x-axis, with x an element of [0, (pi/2)]. Find the volume of the solid, given that the cross sections perpendicular to the x-axis are squares.

Work Shown:

cross sections are squares:

therefore A(x) is not equal to Pi*r^2 rather l^2

therefore A(x)= [sqrt(sin(x)]^2

therefore integral of A(x)dx of x-values from 0 to Pi/2 should provide the answer

I think my approach is wrong and my integral for A(x) dx is wrong as well please help!

 

[galactus]

This is not a revolution problem. You appear to be on the right track.

Since \(\displaystyle y=2\sqrt{sin(x)}\) is a length of a side of the square. It's area is then the square of that

\(\displaystyle (2\sqrt{sin(x)})^{2}=4sin(x)\)

We have \(\displaystyle 4\int_{0}^{\frac{\pi}{2}}sin(x)dx\)

 

[johnq2k7]

This is not a revolution problem. You appear to be on the right track.

Since \(\displaystyle y=2\sqrt{sin(x)}\) is a length of a side of the square. It's area is then the square of that

\(\displaystyle (2\sqrt{sin(x)})^{2}=4sin(x)\)

We have \(\displaystyle 4\int_{0}^{\frac{\pi}{2}}sin(x)dx\)

If I find the integration of the integral you have corrected as : \(\displaystyle 4\int_{0}^{\frac{\pi}{2}}sin(x)dx\)[/quote] will this provide the answer for the Volume of the Region?

 

[Deleted member 4993]

If I find the integration of the integral you have corrected as : \(\displaystyle 4\int_{0}^{\frac{\pi}{2}}sin(x)dx\)

will this provide the answer for the Volume of the Region?[/quote]

What do you think?

Your question tells me that you have not quite understood Glactus's deerivation of the equation.

What does 4*sin(x) represent - a lenght , cross-sectional area, length of flight of bumble-bee - what? How was that expression derived? similarly what does "dx" represent? where did it come from - in this problem?

Please take a pencil and paper and work through the derivation. Then come back to ask question if you do not understand a step.

 

[johnq2k7]

I'm sorry I understand the question now....given that the cross sections are perpendicular to the x-axis are squares.....

4 times the integration of sin(x) should provide the volume of the region... since the simple integration of sin(x) will only provide 1/4 of the volume region...

I understand the question now.. thanks for your help... sorry for my stupid question

 

[Deleted member 4993]

I understand the question now.. thanks for your help... sorry for my stupid question

Your question was not stupid at all - it was just "quick". We do that all the time and get our hand "spanked" for it....

Remember - no question is stupid - just take time to think it through .....