Exam (elaborations)
volume of solids of revolutions
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Finding the volume of the solid obtained by rotating the region enclosed by certain formulas
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KG THWALA MATE1B1 2020Assignment HW9 due 10/16/2020 at 11:59pm SAST
(correct)
1. (1 point) Find the volume of the solid obtained by rotating Correct Answers:
the region enclosed by
• 0
y = x3 , y = 16x, x ≥ 0 • 36
• [pi*(6-y/6)ˆ2-pi*[6-sqrt(y)]ˆ2]*dy
about the line y = 0 using the method of disks or washers.
• pi*6ˆ4/6
Z
Volume = =
4. (1 point) Find the volume of the solid obtained by rotating
Answer(s) submitted:
the region enclosed by
• 0
• 4
y = e4x + 4, y = 0, x = 0, x = 0.3
•
• [65536pi]/21
about the x-axis using the method of disks or washers.
(correct) Z
Correct Answers:
Volume = =
• 0
• 4 Answer(s) submitted:
• [pi*(16*x)ˆ2-pi*(xˆ3)ˆ2]*dx • 0
• 4*4ˆ7*pi/21 • 0.3
•
2. (1 point) Find the volume of the solid obtained by rotating
• 10.693pi
the region enclosed by
(correct)
y = x2 , y = 3x,
Correct Answers:
about the line y = 9 using the method of disks or washers. • 0
Z • 0.3
Volume = = • pi*[eˆ(4*x)+4]ˆ2*dx
Answer(s) submitted: • pi*[(eˆ2.4-1)/8+8*(eˆ1.2-1)/4+4.8]
• 0
• 3 5. (1 point) Find the volume of the solid obtained by rotating
• the region enclosed by
• 48.6pi
(correct) x = 0, y = 1, x = y6
Correct Answers:
• 0 about the line y = 1 using the method of disks or washers.
• 3 Z
• [pi*(9-xˆ2)ˆ2-pi*(9-3*x)ˆ2]*dx Volume = =
• pi*3ˆ5/5
Answer(s) submitted:
3. (1 point) Find the volume of the solid obtained by rotating • 0
the region enclosed by • 1
y = x2 , y = 6x, •
• [1/28]pi
about the line x = 6 using the method of disks or washers.
Z (correct)
Correct Answers:
Volume = =
Answer(s) submitted: • 0
• 1
• 0
• pi*[1-xˆ(1/6)]ˆ2*dx
• 36
• 2*pi/56
•
• 216pi
1
, • pi*5ˆ4/6
6. (1 point) Find the volume of the solid obtained by rotating
the region enclosed by 9. (1 point) Find the volume of the solid obtained by rotating
the region enclosed by
y = x2 , x = 1, x = 3, y=0
y = e5x + 2, y = 0, x = 0, x = 0.7
about the line x = 7 using the method of cylindrical shells.
Z about the y-axis using the method of cylindrical shells.
Volume = = Z
Volume = =
Answer(s) submitted:
Answer(s) submitted:
• 1
• 3 • 0
• • 0.7
• [244pi]/3 •
• 26.368pi
(correct)
Correct Answers: (score 0.10000000149011612)
Correct Answers:
• 1
• 3 • 0
• 2*pi*(7-x)*xˆ2*dx • 0.7
• 2*pi*(7*3ˆ3/3-3ˆ4/4-7*1ˆ3/3+1ˆ4/4) • 2*pi*x*[eˆ(5*x)+2]*dx
• 2*pi*0.7*eˆ(0.7*5)/5-2*pi*eˆ(0.7*5)/(5ˆ2)+2*pi/(5ˆ2)+pi
7. (1 point) Find the volume of the solid obtained by rotating
the region enclosed by 10. (1 point) Find the volume of the solid obtained by rotat-
ing the region enclosed by
y = 36x − 6x2 , y=0
y = ex , x = 0, y=5
about the y-axis using the method of cylindrical shells.
Z about the x-axis using the method of cylindrical shells.
Volume = = Z
Volume = =
Answer(s) submitted:
• 0 Answer(s) submitted:
• 6 •
• •
• 1296pi •
• 88.70584
(correct)
Correct Answers: (correct)
• 0 Correct Answers:
• 6 • 1
• 2*pi*x*(36*x-6*xˆ2)*dx • 5
• pi*6*6ˆ4/6 • 2*pi*y*ln(y)*dy
• pi*5ˆ2*ln(5)-pi*5ˆ2/2+pi/2
8. (1 point) Find the volume of the solid obtained by rotating
the region enclosed by 11. (1 point) Find the volume of the solid obtained by rotat-
2 ing the region enclosed by
y=x , y = 5x 2
y = e−x , y = 0, x = 0, x = 0.7
about the y-axis using the method of cylindrical shells.
Z about the y-axis using the method of cylindrical shells.
Volume = = Z
Answer(s) submitted: Volume = =
• 0 Answer(s) submitted:
• 5 • 0
• • 0.7
• 833.34pi •
(score 0.10000000149011612) •
Correct Answers: (score 0.10000000149011612)
• 0 Correct Answers:
• 5 • 0
• 2*pi*x*(5*x-xˆ2)*dx • 0.7
2
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