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 \({x^2} + {y^2} = 3\).