y1 = 1.4 -2(x-13) , y2 = 1.4 -2(-x+13)
y1 = 27.4 - 2x , y2 = -24.6 + 2x
intersection:
2x - 24.6 = -2x + 27.4
4x = 52
x = 13 , then y = 1.4 ---> range is 0 to 1.4
y1 = 27.4 - 2x ---> x = 13.4 - y/2 --> outer radius
y2 = -24.6 + 2x --> x = 12.3 + y/2 --> inner radius
Volume
= ?? ( (13.4 - y/2)^2 - (12.3 + y/2)^2 ) dy from 0 to 1.4
= ?? (28.27 - 25.7y ) dy from 0 to 1.4
= ?[28.27y - 12.85y^2 ] from 0 to 1.4
= ?( 39.578 - 25.195 - 0)
= ?(14.392)
= appr 45.214 units^3
verification:
http://www.wolframalpha.com/input/?i=%CF%80%E2%88%AB+(+(13.4+-+y%2F2)%5E2+-+(12.3+%2B+y%2F2)%5E2+)+dy+from+0+to+1.4
Use washers to find the volume formed by rotating the region enclosed by:
y=1.4−2|x−13| and y=0 about the y-axis
1 answer
1 answer