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The round is x² + y² + z² = 1

And cone z = 6√(x² + y²)

The volume the the round is

*

Where x,y and also z room in Cartesian coordinates and also Ѳ, φ and also ρ space in Spherical co-ordinate system.

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Where,

x = ρ sin(φ)cos(Ѳ)

y = ρ sin(φ)sin(Ѳ)

z = ρ cos(φ)

then think about

z = 6√(x² + y²)

*

*

*

*

*

*

φ = 9.46°.

Since it is exterior the cone, φ different fom 9.46° come π/2

And

x² + y² + z² = ρ²

Then ρ² = 1

ρ = 1

Therefore ρ varies from 0 to 1.

And Ѳ varies from 0 come 2π.

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Volume of the solid

*

*

Volume of the heavy = 2.065

Therefore Volume the the solid is 2.065.

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