How do you find the volume of the region bounded

Ryan Robertson

Ryan Robertson

Answered question

2022-07-02

How do you find the volume of the region bounded b the line y=x-2, the x-axis, x=2, and x=4 is revolved about the line x=-1?

Answer & Explanation

Sanaa Hinton

Sanaa Hinton

Beginner2022-07-03Added 15 answers

V = π y 1 y 2 ( R 2 r 2 ) d y
y = x 2 , x = 2 y 1 = 2 2 = 0
y = x 2 , x = 4 y 2 = 4 2 = 2
x = 4 R = 4 ( 1 ) = 5
y = x 2 x = y + 2 r = y + 2 ( 1 ) = y + 3
V = π 0 2 ( 5 2 ( y + 3 ) 2 ) d y = π 0 2 ( 25 y 2 6 y 9 ) d y
V = π ( 16 y 3 y 2 y 3 3 ) | 0 2 = π ( 32 12 8 3 )
V = 52 π 3

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