Homework SourseSolve Find the volume of the described solid S The base of S
Solve:
Find the volume of the described solid S. The base of S is the region enclosed by the parabola y=1-x^2 and the x-axis. Cross-sections perpendicular to x-axis are isosceles triangles with height equal to the base.
Find the volume of the described solid S. The base of S is the region enclosed by the parabola y=1-x^2 and the x-axis. Cross-sections perpendicular to x-axis are isosceles triangles with height equal to the base.
Solution
as we know that cross section: base = 2x height = 2x Area = 1/2*(2x)^2 = 2x^2 parabola : y = 1 - x^2 => x^2 = 1 - y vertex at(0 , 1) => upper limit y = 1 x-axis => y = 0 => lower limit y = 0 V = ? 2x^2 dy = 2 ? [y=0 to 1] (1 - y) dy = 2 (y - y^2/2) from 0 to 1 = 2(1 - 1/2) = 1 cubic unit
