The surface area of a right-circular cone of radius r and height h is S = Tr√² +h², and its volume is V = = πr²h. (a) Determine h and r for the cone with given surface area S r = h = = 1 and maximal volume V. (b) What is the ratio h/r for a cone with given volume V = 8 and minimal surface area S? h T (c) Does a cone with given volume V and maximal surface area exist? OA. yes B. no
The surface area of a right-circular cone of radius r and height h is S = Tr√² +h², and its volume is V = = πr²h. (a) Determine h and r for the cone with given surface area S r = h = = 1 and maximal volume V. (b) What is the ratio h/r for a cone with given volume V = 8 and minimal surface area S? h T (c) Does a cone with given volume V and maximal surface area exist? OA. yes B. no
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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![The surface area of a right-circular cone of radius \(r\) and height \(h\) is \( S = \pi r \sqrt{r^2 + h^2} \), and its volume is \( V = \frac{1}{3} \pi r^2 h \).
### (a) Determine \( h \) and \( r \) for the cone with given surface area \( S = 1 \) and maximal volume \( V \):
\[ h = \boxed{} , \quad r = \boxed{} \]
### (b) What is the ratio \( h/r \) for a cone with given volume \( V = 8 \) and minimal surface area \( S \)?
\[ \frac{h}{r} = \boxed{} \]
### (c) Does a cone with given volume \( V \) and maximal surface area exist?
- A. yes
- B. no](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffe70859f-d1ee-4d19-93f5-d3c21b44393e%2Fc689f7fa-82a3-47c3-9fe4-9c5a18b3a3bc%2Fk9jen3h_processed.png&w=3840&q=75)
Transcribed Image Text:The surface area of a right-circular cone of radius \(r\) and height \(h\) is \( S = \pi r \sqrt{r^2 + h^2} \), and its volume is \( V = \frac{1}{3} \pi r^2 h \).
### (a) Determine \( h \) and \( r \) for the cone with given surface area \( S = 1 \) and maximal volume \( V \):
\[ h = \boxed{} , \quad r = \boxed{} \]
### (b) What is the ratio \( h/r \) for a cone with given volume \( V = 8 \) and minimal surface area \( S \)?
\[ \frac{h}{r} = \boxed{} \]
### (c) Does a cone with given volume \( V \) and maximal surface area exist?
- A. yes
- B. no
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