44-46 Use the Theorem of Pappus to find the volume of the given solid. 44. A sphere of radius r (Use Example 4.) 1. EXAMPLE 4 Find the center of mass of a semicircular plate of radius r. yA y=Vr-x² SOLUTION In order to use (8) we place the semicircle as in Figure 11 so that f(x) = vr2 – x² and a = -r, b = r. Here there is no need to use the formula to cal- (o 4r) culate x because, by the symmetry principle, the center of mass must lie on the y-axis, 0, so x = 0. The area of the semicircle is A = Tr', so ỹ = ĀL,[S(x)]*dx bebaiua FIGURE 11 (W - x2)° dx .2 (- x*) dx (since the integrand is even) Tr Jo .3 TTr 3 01 EXERC 2 2r3 4r Tr? 3 Зт The center of mass is located at the point (0, 4r/(3T)).
44-46 Use the Theorem of Pappus to find the volume of the given solid. 44. A sphere of radius r (Use Example 4.) 1. EXAMPLE 4 Find the center of mass of a semicircular plate of radius r. yA y=Vr-x² SOLUTION In order to use (8) we place the semicircle as in Figure 11 so that f(x) = vr2 – x² and a = -r, b = r. Here there is no need to use the formula to cal- (o 4r) culate x because, by the symmetry principle, the center of mass must lie on the y-axis, 0, so x = 0. The area of the semicircle is A = Tr', so ỹ = ĀL,[S(x)]*dx bebaiua FIGURE 11 (W - x2)° dx .2 (- x*) dx (since the integrand is even) Tr Jo .3 TTr 3 01 EXERC 2 2r3 4r Tr? 3 Зт The center of mass is located at the point (0, 4r/(3T)).
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.CT: Test
Problem 9CT
Related questions
Topic Video
Question
number 44 and it says use example 4 so i attached that as well
Transcribed Image Text:44-46 Use the Theorem of Pappus to find the volume of the
given solid.
44. A sphere of radius r (Use Example 4.)
1.
![EXAMPLE 4 Find the center of mass of a semicircular plate of radius r.
yA
y=Vr-x²
SOLUTION In order to use (8) we place the semicircle as in Figure 11 so that
f(x) = vr2 – x² and a = -r, b = r. Here there is no need to use the formula to cal-
(o 4r) culate x because, by the symmetry principle, the center of mass must lie on the y-axis,
0,
so x = 0. The area of the semicircle is A = Tr', so
ỹ =
ĀL,[S(x)]*dx
bebaiua
FIGURE 11
(W - x2)° dx
.2
(- x*) dx
(since the integrand is even)
Tr Jo
.3
TTr
3
01
EXERC
2 2r3
4r
Tr? 3
Зт
The center of mass is located at the point (0, 4r/(3T)).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fee3929bf-b8d7-45ee-b07f-271032dcd794%2Fad782aab-ff4a-4999-9e3f-ad62a2ce9d05%2Fdnznbtw.jpeg&w=3840&q=75)
Transcribed Image Text:EXAMPLE 4 Find the center of mass of a semicircular plate of radius r.
yA
y=Vr-x²
SOLUTION In order to use (8) we place the semicircle as in Figure 11 so that
f(x) = vr2 – x² and a = -r, b = r. Here there is no need to use the formula to cal-
(o 4r) culate x because, by the symmetry principle, the center of mass must lie on the y-axis,
0,
so x = 0. The area of the semicircle is A = Tr', so
ỹ =
ĀL,[S(x)]*dx
bebaiua
FIGURE 11
(W - x2)° dx
.2
(- x*) dx
(since the integrand is even)
Tr Jo
.3
TTr
3
01
EXERC
2 2r3
4r
Tr? 3
Зт
The center of mass is located at the point (0, 4r/(3T)).
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,