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# Consider the region bounded by x=4-y^2, x-axis and y-axis...?

The volume of the solid generated by revolving the region about the x-axis is given by ____ ?

### 2 Answers

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- PopeLv 72 months ago
There are two distinct closed regions having those boundaries, one below the x-axis and one above. They generate the same solid of revolution. It is a paraboloid. Its base radius is 2, and its height is 4.

volume = (1/2)π(2)²(4) = 8π

- micatkieLv 72 months ago
The curve (x = 4 - y²) meets x-axis (y = 0) at (4, 0)

The curve: x = 4 - y² ⇒ y² = 4 - x

Volume of the solid

₄

= ∫ πy²dx

⁰

₄

= ∫ π(4 - x)dx

⁰

₄

= π [4x - (x²/2)]

⁰

= π [4*4 - (4²/2)]

= 8π

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