If a region is bounded by y = x + 3, y=5, and the y=axis...

Kassandra Ross

Kassandra Ross

Answered

2022-06-27

If a region is bounded by y = x + 3, y=5, and the y=axis and it is revolved around the y = 7, how do you find the volume?

Answer & Explanation

assumintdz

assumintdz

Expert

2022-06-28Added 22 answers

The volume of a small slice,
d V = π ( 7 ( x + 3 ) ) 2 d x
Therefore,
V = 0 4 π ( 7 ( x + 3 ) ) 2 d x
V = π 0 4 ( 49 ( x + 6 x + 9 ) ) d x
= π 0 4 ( 49 x 6 x 9 ) d x
= π [ 40 x x 2 2 6 x 2 3 3 2 ] 0 4
= π ( 160 8 32 ) = 120 π

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