FIGURE Q2 shows that the curve x = f(y) divides the rectangle into two areas, A, and A2. y x = k h x = f(y) A1 A2 FIGURE Q2 а. Assume Cup C and Cup D represent solids of revolution. The cups have height, h, and their shapes fit together snugly. Cup C is formed by rotating the curve x = f (y) about the y-axis and Cup D is formed by rotating the same curve about line x = k. By referring to A, and A, from FIGURE Q2, sketch complementary coffee cups for Cup C and Cup D.
FIGURE Q2 shows that the curve x = f(y) divides the rectangle into two areas, A, and A2. y x = k h x = f(y) A1 A2 FIGURE Q2 а. Assume Cup C and Cup D represent solids of revolution. The cups have height, h, and their shapes fit together snugly. Cup C is formed by rotating the curve x = f (y) about the y-axis and Cup D is formed by rotating the same curve about line x = k. By referring to A, and A, from FIGURE Q2, sketch complementary coffee cups for Cup C and Cup D.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
please give a clear explanation according to the questions.
Transcribed Image Text:FIGURE Q2 shows that the curve x = f(y) divides the rectangle into two
areas, A, and A2.
x = k
h
x = f(y)
A1
A2
FIGURE Q2
а.
Assume Cup C and Cup D represent solids of revolution. The cups have
height, h, and their shapes fit together snugly. Cup C is formed by
rotating the curve x = f (y) about the y-axis and Cup D is formed by
rotating the same curve about line x = k. By referring to A, and A, from
FIGURE Q2, sketch complementary coffee cups for Cup C and Cup D.
Transcribed Image Text:b.
Given the equation of the curve x = f(y) is x = Vy +1 and
2 S fy)dy
k
h
suggest a value for h, where h> 0,h E R, then find the total area of
rectangle such that the area A, has to be the same as area A2.
C.
"The two complementary solids of revolution have equal volumes if
and only if the cross sections of those complementary solids have
equal areas"
Based on theorem above and the result obtained in part (ii), calculate
the amount of coffee that each cup holds by using Disk Method and
prove the theorem above.
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