# Math help Cross-section

• May 5th 2009, 08:31 AM
dj41490
Math help Cross-section
The base of each solid below is the region in the xy-plane bounded by the x-axis, the graph x^(1/2) and the line x=3. Fine the volume of the solid. Each cross-section of S4 perpendicular to the y-axis is an isoscelesles right triangles with hypotenuse in the xy-plane

Thank You
• May 5th 2009, 11:03 AM
skeeter
Quote:

Originally Posted by dj41490
The base of each solid below is the region in the xy-plane bounded by the x-axis, the graph x^(1/2) and the line x=3. Fine the volume of the solid. Each cross-section of S4 perpendicular to the y-axis is an isoscelesles right triangles with hypotenuse in the xy-plane

Thank You

$\displaystyle V = \int_c^d A(y) \, dy$

area of an isosceles right triangle with hypotenuse length H, is

$\displaystyle A = \frac{H^2}{4}$

length of a representative hypotenuse perpendicular to the y-axis in the xy plane is ...

$\displaystyle H = 3 - y^2$

so ...

$\displaystyle V = \int_0^{\sqrt{3}} \frac{(3-y^2)^2}{4} \, dy$
• May 5th 2009, 01:31 PM
dj41490
thank you very much