Consider the blue vertical line shown above (click on graph for better view) con
ID: 2857592 • Letter: C
Question
Consider the blue vertical line shown above (click on graph for better view) connecting the graphs y = g(x) = sin(2x)| and y = f(x) = cos(1x)| Referring to this blue line, match the statements below about rotating this line with the corresponding statements about the result obtained. The result of rotating the line about the x-axis is The result of rotating the line about the y-axis is The result of rotating the line about the line y = 1|is The result of rotating the line about the line x = -2| is The result of rotating the line about the line x = pi| is The result of rotating the line about the line y = -2|is The result of rotating the line about the line y = pi| The result of rotating the line about the line y = -pi an annulus with inner radius sin(2x)| and outer radius cos(1x)| a cylinder of radius x + 2|and height cos(1x) - sin(2x)| an annulus with inner radius pi + sin(2x)| an annulus with inner radius 1 - cos(1x) an annulus with inner radius 2 + sin(2x) an annulus with inner radius pi - cos(1x)|and outer radius pi - sin(2x)| a cylinder of radius pi - x| and height cos(1x) - sin(2x)| a cylinder of radius x| and height cos(1x) sin(2x)|Explanation / Answer
This is perfectly solved when you imagine in 3D what's happening for each given case.
One can clearly see that we will have annulus when it is rotated about any y= constant line and we will have a cylinder when it is rotated for x= constant
1-> A ( x-axis implies y=0 , so annulus with radius when y=0 )
2->H ( y-axis implies x=0 , so cylinder with radius = x and height = difference between curves)
3->D (( y=1 , so annulus with radius when y=1 )
4->B ( x=-2 , so cylinder with radius = x+2 and height = difference between curves)
5->G ( x= pi , so cylinder with radius = pi-x and height = difference between curves)
6->E (( y=-2 , so annulus with radius when y=-2 )
7->F (( y=pi , so annulus with radius when y=pi )
8->C (( y=-pi , so annulus with radius when y=-pi )