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Paul
May 6, 2021

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Section 4-9 : Surface Area

1. Determine the surface area of the portion of $$6x + y + 2z = 10$$ that is in the 1st octant.
2. Determine the surface area of the portion of $$4x + 3y + 5z = 8$$ that is inside the cylinder $${x^2} + {y^2} = 49$$ .
3. Determine the surface area of the portion of $$z = 9{x^2} + 9{y^2} - 1$$ that is below the $$xy$$-plane with $$x \le 0$$.
4. Determine the surface area of the portion of $$z = 6y + 2{x^2}$$ that is above the triangle in the $$xy$$-plane with vertices $$\left( {0,0} \right)$$, $$\left( {8,0} \right)$$ and $$\left( {8,2} \right)$$.
5. Determine the surface area of the portion of $$y = 8z + 2{x^3} + 1$$ that is in front of the region in the $$xz$$-plane bounded by $$z = {x^3}$$, $$x = 2$$ and the x-axis.
6. Determine the surface area of the portion of $$x = 6 - {y^2} - {z^2}$$ that is in front of $$x = 2$$ with $$y \ge 0$$.
7. Determine the surface area of the portion of $$y = 4x + 3{z^2}$$ that is in front of the triangle in the $$xz$$-plane with vertices $$\left( {0,0} \right)$$, $$\left( {2,6} \right)$$ and $$\left( {0,6} \right)$$.
8. Determine the surface area of the portion of $$y = 3{x^2} + 3{z^2}$$that is inside the cylinder $${x^2} + {z^2} = 1$$.
9. Determine the surface area of the portion of the sphere of radius 4 that is inside the cylinder $${x^2} + {y^2} = 3$$.