The base of a certain solid is a plane region R enclosed by the x-axis and the curve $y = 1 - x ^ { 2 }$ . Each cross-section of the solid perpendicular to the y-axis is an isosceles right triangle with hypotenuse lying in R. Find the volume of the solid.

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The Answer of The base of a certain solid is a plane region R enclosed by the x-axis and the curve $y = 1 - x ^ { 2 }$ . Each cross-section of the solid perpendicular to the y-axis is an isosceles right triangle with hypotenuse lying in R. Find the volume of the solid.

The Base of a Certain Solid Is a Plane Region y=1−x2y = 1 - x ^ { 2 }y=1−x2

The Base of a Certain Solid Is a Plane Region $y = 1 - x ^ { 2 }$