Find the volumes of the solids generated by revolving the regions bounded by the graphs of the equations about the given lines. y = root x
y = 0
x = 3
the x-axis
the y-axis
the line x = 3
the line x = 6

x-axis =

y-axis =

Line x =3 :  

Line x = 6 :

Step-by-step explanation:

Given lines : y = √x

                     y = 0

                     x = 3

To determine the volumes generated we will use the disk method for each of the lines,

attached below is the detailed solution for  line x =3 , same procedure will be repeated for each value of x and y to obtain the given results

The volume generated  ( x axis )

=

volume generated ( y _axis )

=  

Volume about  x = 3

=  

Volume about  x = 6

=

option 1

data plot with   3 dots over 33, 1 dot over 34, 2 dots over 35, no dot over 36, 1 dot over 37, 2 dots over 38, 4 dots over 39, and 2 dot over 40.

8(-10x+3.5y-7)

8×-10x + 8×3.5y + 8×-7

-80x + 28y - 56

therefore

-80x+28y-56 is the correct answer