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May 6, 2021

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### Section 4-9 : Surface Area

1. Determine the surface area of the portion of $$2x + 3y + 6z = 9$$ that is in the 1st octant. Solution
2. Determine the surface area of the portion of $$z = 13 - 4{x^2} - 4{y^2}$$ that is above $$z = 1$$ with $$x \le 0$$ and $$y \le 0$$. Solution
3. Determine the surface area of the portion of $$\displaystyle z = 3 + 2y + \frac{1}{4}{x^4}$$ that is above the region in the $$xy$$-plane bounded by $$y = {x^5}$$, $$x = 1$$ and the $$x$$-axis. Solution
4. Determine the surface area of the portion of $$y = 2{x^2} + 2{z^2} - 7$$that is inside the cylinder $${x^2} + {z^2} = 4$$. Solution
5. Determine the surface area region formed by the intersection of the two cylinders $${x^2} + {y^2} = 4$$ and $${x^2} + {z^2} = 4$$. Solution