how can we find the volume between the two curves??

Question

anonymous · Answer

Since curves are 2 dimensional and volume is 3 dimensional, it won't work.  It's like trying to find the area between two points... doesn't make sense.  Do you mean the area between two curves or the volume between two surfaces..?

abb0t · Answer

I think you are referring to volumes of solids of revolutios. First let me define just what a solid of revolution is.  
To get a solid of revolution we start out with a function, f(x) , on an interval [a,b].|dw:1356382598164:dw|
rotating about the x-axis gives a 3-dimensional region. What you are usually asked to do for these is find the volume of this object, given by the derived area and volume formula's:
$$V = \int\limits_{a}^{b} A(x)dx$$ or $$V = \int\limits_{c}^{d} A(y)dy$$
where A(x) and A(y) is the cross-sectional area of the solid.
One of the easier methods for getting the cross-sectional area is to cut the object perpendicular to the axis of rotation. Doing this the cross section will be either a solid disk if the object is solid (as our above example is) or a ring if we’ve hollowed out a portion of the solid.
In the case that we get a solid disk the area is:
$$A = \pi (radius)^2$$ where the radius will depend upon the function and the axis of rotation.
Hence, we can get it for a ring:
$$A = \pi ((outer.radius)^2-(inner.radius)^2)$$
where again both of the radii will depend on the functions given and the axis of rotation.