AP Calculus BC Quiz
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CONTEXTUAL APPLICATIONS OF DIFFERENTIATION
Question 1
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A spherical balloon's radius
r
r
r
increases over time; with
V
=
4
3
π
r
3
V=\frac{4}{3}\pi r^3
V
=
3
4
π
r
3
, which related-rates setup is correct?
A
d
V
d
t
=
4
π
r
3
d
r
d
t
\dfrac{dV}{dt}=4\pi r^3\dfrac{dr}{dt}
d
t
d
V
=
4
π
r
3
d
t
d
r
B
d
V
d
t
=
4
π
r
2
d
r
d
t
\dfrac{dV}{dt}=4\pi r^2\dfrac{dr}{dt}
d
t
d
V
=
4
π
r
2
d
t
d
r
C
d
V
d
t
=
4
3
π
d
r
d
t
\dfrac{dV}{dt}=\dfrac{4}{3}\pi\dfrac{dr}{dt}
d
t
d
V
=
3
4
π
d
t
d
r
D
d
V
d
t
=
4
π
r
2
\dfrac{dV}{dt}=4\pi r^2
d
t
d
V
=
4
π
r
2
E
d
V
d
t
=
4
3
π
r
3
\dfrac{dV}{dt}=\dfrac{4}{3}\pi r^3
d
t
d
V
=
3
4
π
r
3
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