x² 11) Find a parametrization of the surface S which is the portion of the cone - + 25 25 and z = 3. Find the area element. Then find the surface area of S. z² 16 that lies between z = = 2 (5 marks)
x² 11) Find a parametrization of the surface S which is the portion of the cone - + 25 25 and z = 3. Find the area element. Then find the surface area of S. z² 16 that lies between z = = 2 (5 marks)
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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![### Problem 11: Parametrization and Surface Area of the Cone Segment
Find a parametrization of the surface \( S \), which is the portion of the cone described by:
\[
\frac{x^2}{25} + \frac{y^2}{25} = \frac{z^2}{16}
\]
that lies between \( z = 2 \) and \( z = 3 \). First, determine the area element. Then, find the surface area of \( S \).
**Worth:** 5 marks](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F01de6821-244f-42f2-a644-d1243544b623%2F988a5184-782e-46ba-80ca-4b185d9141e6%2Fp4fd7r_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem 11: Parametrization and Surface Area of the Cone Segment
Find a parametrization of the surface \( S \), which is the portion of the cone described by:
\[
\frac{x^2}{25} + \frac{y^2}{25} = \frac{z^2}{16}
\]
that lies between \( z = 2 \) and \( z = 3 \). First, determine the area element. Then, find the surface area of \( S \).
**Worth:** 5 marks
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