# Math Help - Math help Cross-section

1. ## 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

2. 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
$V = \int_c^d A(y) \, dy$

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

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

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

$H = 3 - y^2$

so ...

$V = \int_0^{\sqrt{3}} \frac{(3-y^2)^2}{4} \, dy$

3. thank you very much