The volume of a solid above the square and below the elliptic paraboloid is to be estimated by dividing the square R into 9 equal squares and selecting sample points in the center of each square. We know that, R = [0,1] × [0,1]Divide each interval into three equal subintervals, then the subinterval lengths are Δx = 1/3 and Δy = 1/3. Thus, the sample points are as follows:(1/6, 1/6), (1/6, 1/2), (1/6, 5/6)(1/2, 1/6), (1/2, 1/2), (1/2, 5/6)(5/6, 1/6), (5/6, 1/2), (5/6, 5/6)Using these sample points, we can compute the volume of each of the corresponding rectangular parallelepipeds using the formula Volume of rectangular parallelepiped = ∆V ≈ f(xi,yi) ∆x ∆y.Then, the approximated value of the volume of the solid is as follows.∆V1 ≈ f(1/6,1/6) ∆x ∆y = [100 - (1/6)² - 6(1/6)(1/6) - (1/6)²] 1/9∆V2 ≈ f(1/6,1/2) ∆x ∆y = [100 - (1/6)² - 6(1/6)(1/2) - (1/2)²] 1/9∆V3 ≈ f(1/6,5/6) ∆x ∆y = [100 - (1/6)² - 6(1/6)(5/6) - (5/6)²] 1/9∆V4 ≈ f(1/2,1/6) ∆x ∆y = [100 - (1/2)² - 6(1/2)(1/6) - (1/6)²] 1/9∆V5 ≈ f(1/2,1/2) ∆x ∆y = [100 - (1/2)² - 6(1/2)(1/2) - (1/2)²] 1/9∆V6 ≈ f(1/2,5/6) ∆x ∆y = [100 - (1/2)² - 6(1/2)(5/6) - (5/6)²] 1/9∆V7 ≈ f(5/6,1/6) ∆x ∆y = [100 - (5/6)² - 6(5/6)(1/6) - (1/6)²] 1/9∆V8 ≈ f(5/6,1/2) ∆x ∆y = [100 - (5/6)² - 6(5/6)(1/2) - (1/2)²] 1/9∆V9 ≈ f(5/6,5/6) ∆x ∆y = [100 - (5/6)² - 6(5/6)(5/6) - (5/6)²] 1/9Add up the volumes of the rectangular parallelepipeds to get the approximated volume of the solid.∆V1 + ∆V2 + ∆V3 + ∆V4 + ∆V5 + ∆V6 + ∆V7 + ∆V8 + ∆V9 = 1/9[100 - 1/36 - 1/36 - 1/36 - 1/4 - 5/36 - 25/36 - 5/36 - 25/36]≈ 6.847Therefore, the approximated volume of the solid is 6.847.