Surface Area

(requires JavaScript)

  1. Find the area of the part of the plane z=2+3x+4y that is above the rectangle 05×14 .
    1526
  2. Find the area of the part of the hyperbolic paraboloid z=y2x2 that is between the cylinders y2+x2=1 and y2+x2=4 .
    π6171755
  3. Find the area of the part of the surface z=1+3x+2y2 that is above the triangle with vertices 00 , 01 , and 21 .

  4. Find the area of the part of the surface y=4x+z2 that is between the planes x=0 , x=1 , z=0 , and z=1 .
    212+174ln2+21ln17
  5. Use the Midpoint Rule for double integrals with 6 squares to estimate the area of the surface z=11+x2+y2 , 0x6 , 0y4 .
    Approximately 24.2055
  6. Find the area of the surface obtained by rotating the curve y=x , 4x9 , about the x-axis .
    π637371717