PROBLEM 5.48*
Determine by direct integration the centroid of the area shown.
PROBLEM 5.48* (Continued)
PROBLEM 5.49*
Determine by direct integration the centroid of the area shown.
PROBLEM 5.50
Determine the centroid of the area shown in terms of a.
PROBLEM 5.51
Determine the centroid of the area shown when a = 4 in.
PROBLEM 5.52
Determine the volume and the surface area of the solid obtained by rotating
the area of Prob. 5.1 about (a) the x axis, (b) the line x = 72 mm.
PROBLEM 5.53
Determine the volume and the surface area of the solid obtained by rotating the
area of Problem 5.2 about (a) the x-axis, (b) the y-axis.
PROBLEM 5.54
Determine the volume and the surface area of the solid obtained by rotating the
area of Problem 5.6 about (a) the line x 60 mm, (b) the line y 120 mm.
x
line line
11 2 2 3 3
Area 2 2 ( )
2( )
2(60) (60) 2(60) (60)
2 60 60 (60)(120)
22
xL x L
xL xL xL
where
123
,,
x
xx are measured with respect to line 60 mm.x
32
Area 116.3 10 mm
(b) Rotation about line 120 mm:y
3
Volume 2(120 ) 2(120 )
2 [120(7200) 629.83 10 ]
yA A yA
63
Volume 1.471 10 mm
line line
11 22 44
Area 2 2 ( )
2( )
y
LyL
y
LyLyL
where
124
,,yyy are measured with respect to line 120 mm.y
2(60) (60) 2(60) (60)
Area 2 120 (60)(120)
22
32
Area 116.3 10 mm
PROBLEM 5.55
Determine the volume and the surface area of the chain link
shown, which is made from a 6-mm-diameter bar, if R 10 mm
and L 30 mm.
PROBLEM 5.56
Determine the volume of the solid generated by rotating the
parabolic area shown about (a) the x-axis, (b) the axis AA.