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Mathematics
Problem
A glass bowl is formed by rotating the curve
x
=
y
2
x = y^{2}
x
=
y
2
for
0
≤
y
≤
2
0 \le y \le 2
0
≤
y
≤
2
about the
y
y
y
-axis. A second bowl is formed by rotating the curve
x
=
2
y
x = 2y
x
=
2
y
for
0
≤
y
≤
2
0 \le y \le 2
0
≤
y
≤
2
about the
y
y
y
-axis. Which bowl has the greater volume, and by how much?
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