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Let V be the volume of the solid obtained by rotating about the y-axis the region bounded y = 25x and y = 을 Find V by slicing. 25 V= Draw a diagram to explain your method. y у 25 25 20 20 15 15 10 10 X х -20 -10 10 20 20 -- 10 10 20 y у 25 25 20 20 15 15 10 10 5F 5 - 20 LUX 20 X -10 10 O -- 20 -10 10 20 Find V by cylindrical shells. V =
Draw a diagram to explain your method. у 25 25 2017 20 15 10 5 X - 20 О. - 10 10 20 --20 - 10 10 20 y y 25 25 20 20 15 10 -54 x -20 -10 X 10 20 o - 20 -10 10 20
Let S be the solid obtained by rotating the region shown in the figure about the y-axis. (Assume a = 9 and b = 3.) y = a sin(bx 0 . VT/b Sketch a typical approximating shell. у 3.0 у 101 2.5 5 2.0 A 1.5 0.5 1.0 1.5 -5 1.0 0.5 5-107 - 1.0 0.5 1.0 у y O 3
y 101 y 3 2 6 1 A х 0.2 0.4 4 0.6 0.8 1.0 -1 - 2 2 3 O هههها X 1.5 -1.5 - 1.0 1.0 Find its circumference c and height h. c(x) = h(x) = Use shells to find the volume V of S. V =
Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curves about the x-axis. 24y2 - 8y3, x = 0 V=
Sketch the region and a typical shell. у у 3 2 30 20 10 20 30 10 - 2 --3 - 2 - 1 У у 30 20 Х 10 20 30 10 х -3 2 2 3