Posted by **Jack** on Sunday, November 21, 2010 at 8:20pm.

Calculate the volume of the ramp in Figure 17 in three ways by integrating the area of the cross sections:

(a) Perpendicular to the x-axis (rectangles)

(b) Perpendicular to the y-axis (triangles)

(c) Perpendicular to the z-axis (rectangles)

- Calculus -
**MathMate**, Sunday, November 21, 2010 at 9:29pm
We do not see the figure, but could probably help anyway.

Along whichever axis you do the integration, the method is to cut up the volume into slices perpendicular to the x-axis, say. Each slice is of thickness dx and the width and height will be a function of y and z, which should in turn be transformed to a function of x. Do the integration along the x-axis and find the volume.

You can proceed in a similar way along the two other axes. The resulting volumes should, of course, be identical.

## Answer This Question

## Related Questions

- Math - Calculate the volume of the ramp in Figure 17 in three ways by ...
- calc - The base of a three-dimensional figure is bound by the line y = 6 - 2x on...
- Calculus - R is the region in the plane bounded below by the curve y=x^2 and ...
- Calculus - R is the region in the plane bounded below by the curve y=x^2 and ...
- Calculus - R is the region in the plane bounded below by the curve y=x^2 and ...
- Calculus - Let f and g be the functions given by f(x)=1+sin(2x) and g(x)=e^(x/2...
- Calculus - Find the volume of the solid obtained by rotating the region bounded ...
- Calculus - Find the volume of the solid obtained by rotating the region bounded ...
- Calculus - Find the volume of the solid obtained by rotating the region bounded ...
- calculus - The base of a solid is a circle of radius = 4 Find the exact volume ...

More Related Questions