The volume of the solid is 900 cubic unit given that the solid lies between planes perpendicular to the x-axis at x = 0 and x = 19, the cross sections perpendicular to the x-axis on the interval 0 ≤ x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x. This can be obtained by finding the area of the square using the length of the diagonal.
Given that, diagonals that run from the parabola y = - 2√x to the parabola y = 2√x
D = 2√x - (-2√x)
D = 4√x
D² = s² + s², where s is the side of the square
(4√x)² = 2s²
16x = 2s²
s² = 8x
s² is the area
Thus,
V = [tex]\int\limits^{15}_0 {8x} \, dx[/tex]
V = [tex]8\int\limits^{15}_0 {x} \, dx[/tex]
V = 4 (15² - 0)
V = 4×225
⇒ V = 900 cubic unit
Hence the volume of the solid is 900 cubic unit given that the solid lies between planes perpendicular to the x-axis at x = 0 and x = 19, the cross sections perpendicular to the x-axis on the interval 0 ≤ x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x.
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Question: A solid lies between planes perpendicular to the x-axis at x = 0 and x = 19. The cross sections perpendicular to the x-axis on the interval 0 ≤x ≤ 15 are squares with diagonals that run from the parabola y = - 2√x to the parabola y = 2√x. Find the volume of the solid.
