Volumes with Cross Sections: Triangles/Semicircles
AP Calculus AB · Flashcards · Application
AP CALCULUS AB · FLASHCARDS
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QUESTION
What is the integral for the volume of a solid with triangular cross sections of base
b
b
b
?
QUESTION
Find the diameter
d
(
x
)
d(x)
d
(
x
)
if the base region is between
y
=
x
y=\sqrt{x}
y
=
x
(top) and
y
=
x
y=x
y
=
x
(bottom).
QUESTION
What is
A
(
x
)
A(x)
A
(
x
)
for a semicircle if the radius is
r
(
x
)
=
x
+
1
r(x)=x+1
r
(
x
)
=
x
+
1
?
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ANSWER
A
(
x
)
=
π
2
(
x
+
1
)
2
A(x)=\frac{\pi}{2}(x+1)^2
A
(
x
)
=
2
π
(
x
+
1
)
2
. Substitutes
r
=
x
+
1
r=x+1
r
=
x
+
1
into semicircle area formula
A
=
π
2
r
2
A=\frac{\pi}{2}r^2
A
=
2
π
r
2
.
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