Wednesday

August 20, 2014

August 20, 2014

Posted by **Sam** on Saturday, January 15, 2011 at 9:05pm.

(a) What is the volume of the solid generated when revolving this region about the line y=16 ?

- calculus -
**bobpursley**, Saturday, January 15, 2011 at 9:17pmfirst sketch it. then determine where the y=16 line intersects (-4,16)(4,16)

Now, lets integrate from the parabola to the line

dArea=dx*(16-y)=(16-x^2)dx

area= INT (16-x^2)dx from x=-4 to 4

area= [16x-1/3 x^3] over the limits

area= 16*4-1/3 4^3 - 16(-4)+1/3 (-4)^3

=2(16*4 - 1/3 4^3)

and you can finish it.

You could have recognized symettry, and just integrated from x=0 to 4, then doubled the area.

**Related Questions**

Calculus - Find the volume of the solid generated by revolving the region ...

math - 1) A region is bounded by the line y = x and the parabola y = x2 - 6x + ...

math - 1) A region is bounded by the line y = x and the parabola y = x2 - 6x + ...

calculus - Find the volume of the solid generated by revolving the region about ...

Calculus - Find the volume of the solid generated by revolving the following ...

calculus - Find the volume of the solid generated by revolving about line x = -4...

calculus - determine the volume of the solid of revolution generated by ...

calculus - Find the volume of the solid generated by revolving the region about ...

calculus - Use the disk or the shell method to find the volume of the solid ...

Math (Calculus) - Use the disc method to find the volume of the solid generated ...