Nikita Sharma 2019W2 MATH 101 209
Assignment Homework 4 due 9/12/14 at 9pm
1. (1 point)
The volume of the solid obtained by rotating the region en- Hint
closed by Correct Answers:
y = x3 , y = 36x, x ≥ 0
• pi*pi/(4*1) + 2*8*pi/1
about the line y = 0 can be computed using vertical slices via an
integral
5. (1 point) Find the volume of the√
solid obtained by rotating
Z b the region bounded by y = x and y = x about the line x = 3.
V= ? Volume =
a
Correct Answers:
with limits of integration a = and b = . • pi*(3/3-2/15)
The volume is V = cubic units.
Note: You can earn full credit if the last question is correct 6. (1 point)
and all other questions are either blank or correct. A spring has a natural length of 20 cm. If a 25-N force is re-
Correct Answers: quired to keep it stretched to a length of 30 cm, how much work
• pi*((36*x)**2) - pi*((x**3)**2) (in J) is required to stretch it from 20 cm to 25 cm?
• DX Work done = J
• 0 Correct Answers:
• 6
• 0.3125
• 167513.310681012
2. (1 point)
7. (1 point)
Using vertical slices, find the volume of the √
solid obtained
If 6 J of work are needed to stretch a spring from 10 cm to 12
by rotating the region bounded by the curves y = x − 1, y = 0,
cm and another 10 J are needed to stretch it from 12 cm to 14
x = 2, and x = 6 about the x-axis.
cm, what is the natural length (in cm) of the spring?
Volume =
Correct Answers:
Natural length of the spring = cm
Correct Answers:
• pi*((6)ˆ2/2-6)
• 8
3. (1 point)
Using horizontal slices, find the volume of the solid obtained
by rotating the region bounded by 8. (1 point)
A particle is moved along the x-axis by a force that measures
x = 8y2 , y = 1, x = 0 10/(1 + x)2 N at a point x metres from the origin. Find the work
(in joules) done in moving the particle from the origin to a dis-
about the y-axis.
tance of 9 metres.
Work done = joules
Answer: Correct Answers:
Correct Answers:
• 8*8*pi/5 • 9
4. (1 point)
Find the volume of the solid obtained by rotating the region 9. (1 point)
bounded by A cable that weighs 2 kg/m is used to lift 800 kg of coal up a
mineshaft 500 m deep. Find the work done (in joules). Use the
value 9.8 m/s2 for the acceleration due to gravity.
y = 0, y = cos(1x), x = π/2, x = 0
Work done = joules
about the line y = −8 Correct Answers:
• 650000*9.8
Answer:
1
Assignment Homework 4 due 9/12/14 at 9pm
1. (1 point)
The volume of the solid obtained by rotating the region en- Hint
closed by Correct Answers:
y = x3 , y = 36x, x ≥ 0
• pi*pi/(4*1) + 2*8*pi/1
about the line y = 0 can be computed using vertical slices via an
integral
5. (1 point) Find the volume of the√
solid obtained by rotating
Z b the region bounded by y = x and y = x about the line x = 3.
V= ? Volume =
a
Correct Answers:
with limits of integration a = and b = . • pi*(3/3-2/15)
The volume is V = cubic units.
Note: You can earn full credit if the last question is correct 6. (1 point)
and all other questions are either blank or correct. A spring has a natural length of 20 cm. If a 25-N force is re-
Correct Answers: quired to keep it stretched to a length of 30 cm, how much work
• pi*((36*x)**2) - pi*((x**3)**2) (in J) is required to stretch it from 20 cm to 25 cm?
• DX Work done = J
• 0 Correct Answers:
• 6
• 0.3125
• 167513.310681012
2. (1 point)
7. (1 point)
Using vertical slices, find the volume of the √
solid obtained
If 6 J of work are needed to stretch a spring from 10 cm to 12
by rotating the region bounded by the curves y = x − 1, y = 0,
cm and another 10 J are needed to stretch it from 12 cm to 14
x = 2, and x = 6 about the x-axis.
cm, what is the natural length (in cm) of the spring?
Volume =
Correct Answers:
Natural length of the spring = cm
Correct Answers:
• pi*((6)ˆ2/2-6)
• 8
3. (1 point)
Using horizontal slices, find the volume of the solid obtained
by rotating the region bounded by 8. (1 point)
A particle is moved along the x-axis by a force that measures
x = 8y2 , y = 1, x = 0 10/(1 + x)2 N at a point x metres from the origin. Find the work
(in joules) done in moving the particle from the origin to a dis-
about the y-axis.
tance of 9 metres.
Work done = joules
Answer: Correct Answers:
Correct Answers:
• 8*8*pi/5 • 9
4. (1 point)
Find the volume of the solid obtained by rotating the region 9. (1 point)
bounded by A cable that weighs 2 kg/m is used to lift 800 kg of coal up a
mineshaft 500 m deep. Find the work done (in joules). Use the
value 9.8 m/s2 for the acceleration due to gravity.
y = 0, y = cos(1x), x = π/2, x = 0
Work done = joules
about the line y = −8 Correct Answers:
• 650000*9.8
Answer:
1
