Calculus III - Surface Area (Assignment Problems)

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Section 15.9 : Surface Area

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