Mathematics, 02.03.2020 17:44 sswaqqin
Find the volume of the solid whose base is the region in the first quadrant bounded by y=x3, y=1, and the y-axis and whose cross-sections perpendicular to the x axis are semicircles.
Answers: 2
![\mathbf{V = \frac{\pi}{8} [(1 - \frac{1^4}{2} + \frac{1^7}{7}) - (0 - \frac{0^4}{2} + \frac{0^7}{7})]}](/tpl/images/0530/2362/9e0d3.png)
![\mathbf{V = \frac{\pi}{8} [(1 - \frac{1}{2} + \frac{1}{7}) ]}](/tpl/images/0530/2362/5c79b.png)
![\mathbf{V = \frac{\pi}{8} [\frac{14 - 7 + 2}{14} ]}](/tpl/images/0530/2362/1d73a.png)
![\mathbf{V = \frac{\pi}{8} [\frac{9}{14} ]}](/tpl/images/0530/2362/d856b.png)
in the interval [0, 1], the corresponding cross-section is a semicircle with diameter 
, so the area of the cross-section would be 
.
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Find the volume of the solid whose base is the region in the first quadrant bounded by y=x3, y=1, an...
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