integral volume: Let G be the parabolic region bounded by...

[mathhelp]

Let G be the parabolic region in the x-y plane bounded below by the curve y=x^2 and above by the line y=1.

a) Suppose a solid has a base G and the cross-sections of the solid perpendicular to the y-axis are squares. Sketch the solid and find its volume.

b) Suppose a solid has a base G and the cross-sections of the solid perpendicular to the y-axis are equilateral triangles. Sketch the solid and find its volume.

Thank you for helping.

 

[galactus]

Re: integral volume

Let G be the parabolic region in the x-y plane bounded below by the curve y=x^2 and above by the line y=1.

a) Suppose a solid has a base G and the cross-sections of the solid perpendicular to the y-axis are squares. Sketch the solid and find its volume.

Where are you hung up?. What are your efforts?. Any ideas?.

Can you set up the region as an integral?. You know the area of a square formula, don't you?. It's just x^2, if a side of the square is x. Now, what would you do with your integral once you set it up?.

[quote:2153tjb9]b) Suppose a solid has a base G and the cross-sections of the solid perpendicular to the y-axis are equilateral triangles. Sketch the solid and find its volume.

Same premise as before except the area of an equilateral triangle is

\(\displaystyle A=\frac{\sqrt{3}}{4}x^{2}\).

Thank you for helping.[/quote:2153tjb9]