Mathematics, 12.03.2020 05:39 minelly1717
Find the volume V of the described solid S. The base of S is the triangular region with vertices (0, 0), (2, 0), and (0, 2). Cross-sections perpendicular to the y-axis are equilateral triangles.
Answers: 3
![V=\int\limits^2_0 {\frac{\sqrt{3} }{4} } s^2\, dx \\=\frac{\sqrt{3} }{4} \int\limits^2_0 {(-y+1)^2} \, dx \\=\frac{\sqrt{3} }{4} \int\limits^2_0 {(y^2-2y+1)} \, dx \\=\frac{\sqrt{3} }{4} [\frac{1}{3} y^3-y^2+y]\\=\frac{\sqrt{3} }{4} [\frac{1}{3} (2)^3-(2)^2+2)]\\=5.48](/tpl/images/0544/5738/a1c86.png)
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Find the volume V of the described solid S. The base of S is the triangular region with vertices (0,...
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