PROBLEM 5.122
Determine by direct integration the values of
x
for the two volumes obtained by passing a vertical
cutting plane through the given shape of Figure 5.21. The cutting plane is parallel to the base of the given
shape and divides the shape into two volumes of equal height.
A hemisphere
PROBLEM 5.122 (Continued)
24
22 2
a
a
xx
PROBLEM 5.123
Determine by direct integration the values of
x
for the two volumes obtained by passing a vertical
cutting plane through the given shape of Figure 5.21. The cutting plane is parallel to the base of the given
shape and divides the shape into two volumes of equal height.
A semiellipsoid of revolution
PROBLEM 5.123 (Continued)
22 2
2
EL
2
PROBLEM 5.124
Determine by direct integration the values of
x
for the two volumes obtained by passing a vertical
cutting plane through the given shape of Figure 5.21. The cutting plane is parallel to the base of the given
shape and divides the shape into two volumes of equal height.
A paraboloid of revolution
PROBLEM 5.124 (Continued)
PROBLEM 5.125
Locate the centroid of the volume obtained by rotating the shaded area
about the x-axis.
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PROBLEM 5.126
Locate the centroid of the volume obtained by rotating the shaded area
about the x-axis.
PROBLEM 5.127
Locate the centroid of the volume obtained by rotating the shaded
area about the line
.xh
PROBLEM 5.127 (Continued)
22
22
a
h