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KIPPAP EDUCATION
17 Related Rates
INSTRUCTION: Select the correct answer for each of the following questions.
Mark only one answer for each item by shading the box corresponding to the
letter of your choice on the answer sheet provided. STRICTLY NO ERASURES
ALLOWED.
1. The radius of an expanding sphere changes at the rate of 2 cm per minute.
How fast is the surface area of the sphere changing when the radius is 25
cm, in cm^2/min?
A. 1244.52
C. 1256.64
B. 1165.45
D. 1464.56
2. A balloon is rising vertically over a point a on the ground at the rate
of 15 ft/sec. A point b is on the ground level 30 ft from a. When the balloon
is 40 ft from a, at what rate is its distance from b changing?
A. 10 ft/sec
C. 15 ft/sec
B. 14 ft/sec
D. 12 ft/sec
3. Two railroad tracks are perpendicular to each other. At 12 PM there is a
train at each track approaching the crossing at 50 kph, one being 100 km and
the other being 150 km away from the crossing. How fast in kph is the distance
between the two trains changing at 4 PM?
A. 57.09 kph
C. 61.07 kph
B. 78.17 kph
D. 67.08 kph
4. A man walks across a bridge at a rate of 5 ft/s as a boat directly beneath
him passes at 10 ft/s. If the bridge is 10 ft above the boat, how fast are
the man and the boat separating 1 second later?
A. 6.23 ft/s
C. 9.33 ft/s
B. 8.33 ft/s
D. 5.32 ft/s
5. A rectangular trough is 10 ft long and 3 ft wide. Find how fast the
surface rises, if water flows in at the rate of 12 ft^3/min.
A. 0.1 ft/min
C. 0.2 ft/min
B. 0.4 ft/min
D. 0.8 ft/min
6. A meteorologist is inflating a spherical balloon. If the radius of the
balloon is changing at a rate of 1.5 cm/second, express the volume V of the
balloon as a function of time t (in seconds).
A. V(t) = 4.5*π*t^3
C. V(t) = (4/3)*π*t^3
B. V(t) = 1.5*π*t^3
D. V(t) = 4*π*t^3
7. A particle moving along the curve y = √(x). As the particle passes through
the point (4, 2), its x-coordinate increases at the rate of 3 cm/s. How fast
is the distance from the particle to the origin changing at this instant?
A. 2.01 cm/s
C. 3.15 cm/s
B. 4.13 cm/s
D. 3.02 cm/s
Kippap Education
0905 664 2628
kippapeducation@gmail.com
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CE Board Exam Review
lOMoARcPSD|35136302
KIPPAP EDUCATION
17 Related Rates
8. Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet
per minute so that it forms a pile in the shape of a cone whose height and
base are always equal. How fast is the height of the pile increasing when
the pile is 10 ft high?
A. 0.238 ft/min
C. 0.493 ft/min
B. 0.382 ft/min
D. 0.271 ft/min
9. A particle moves according to the equation s = t^4 + 6t^3 - 12t^2 + C,
where t is in seconds and S in meters. What time t will the particle come to
rest?
A. 1.016 seconds
C. 1.076 seconds
B. 1.035 seconds
D. 1.057 seconds
10. In the previous question, what is the range of values of t when the
particle's speed is increasing?
A. t ≥ 0.562 seconds
C. t ≥ 0.673 seconds
B. t ≥ 0.451 seconds
D. t ≥ 0.256 seconds
Kippap Education
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kippapeducation@gmail.com
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CE Board Exam Review
lOMoARcPSD|35136302
17
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