2) Suppose that a barrel with maximum radius R and height h can be constructed by rotating a parabola about the x-axis. The parabola is defined as: h h y =R-cr', -sxs 2 where c is a positive constant. (a) Sketch the curve and show that the radius of each end of the barrel is r = R-d where d = ch? (b) Show that the volume of the barrel is V =-nh 2R +r?
2) Suppose that a barrel with maximum radius R and height h can be constructed by rotating a parabola about the x-axis. The parabola is defined as: h h y =R-cr', -sxs 2 where c is a positive constant. (a) Sketch the curve and show that the radius of each end of the barrel is r = R-d where d = ch? (b) Show that the volume of the barrel is V =-nh 2R +r?
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Question
![2) Suppose that a barrel with maximum radius R and height h can be constructed by rotating
a parabola about the x-axis. The parabola is defined as:
h
y = R-cx', -s:
2
where c is a positive constant.
(a) Sketch the curve and show that the radius of each end of the barrel is
r = R– d
ch2
where d =
(b) Show that the volume of the barrel is
1
V =÷th| 2R² +r?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74fc30aa-fbe1-4699-9737-908ff27b5ddb%2Fca6d1467-2657-43fd-ade8-688da4ec8085%2Fzy8936j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2) Suppose that a barrel with maximum radius R and height h can be constructed by rotating
a parabola about the x-axis. The parabola is defined as:
h
y = R-cx', -s:
2
where c is a positive constant.
(a) Sketch the curve and show that the radius of each end of the barrel is
r = R– d
ch2
where d =
(b) Show that the volume of the barrel is
1
V =÷th| 2R² +r?
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