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Practice Test IV A for Math 1501, Calculus I
Problem 1:
A two dimensional domain is bounded by the positive
x
axis, the positive
y
axis and the curve
√
x
+
√
y
=
√
a
.
a) Sketch this domain.
b) Compute its center of mass. (assume that the mass density is uniform).
c) Rotating this shape about the
x
=
y
axis yields a solid. Compute the volume of
that solid.
d) Rotating this shape about the
x
=

y
axis yields another solid. Compute the
volume of that solid.
Problem 2:
The great pyramid has a square base of about 250 m by 250 m. Its height is
about 150 m . Suppose the stone used in its construction weighs 5000 kg per cubic meter.
(
g
=10
m/s
2
).
a) How much work was done to lift all the rock into place during its construction?
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 Fall '08
 N/A
 Calculus

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