Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
![**Find the volume of the largest right circular cylinder that fits in a sphere of radius 1.**
### Diagram Explanation:
The diagram shows a sphere with a larger black circle representing its boundary. Inside the sphere is a magenta-colored right circular cylinder inscribed within.
- **h:** The height of the cylinder, shown as a vertical line parallel to the sides of the cylinder.
- **r:** The radius of the cylinder's base, depicted on the top circle inside the cylinder.
- **R:** The radius of the sphere, with a value of 1, shown as a blue line extending from the center of the sphere to the edge of the sphere.
The diagram illustrates the relationship between the cylinder and the sphere in which it is inscribed.
### Objective:
Calculate the volume (V) of this cylinder, considering the constraint that it fits perfectly within the sphere. The volume is represented by the formula:
\[ V = \text{___} \]
You need to fill in this blank with the calculated volume of the cylinder based on the given conditions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04fa31ea-1ca2-4b00-bba0-bdc1e16393b7%2F7862e296-e7bf-4ba5-b869-c28a836a85c9%2Fw6dixb_processed.png&w=3840&q=75)
Transcribed Image Text:**Find the volume of the largest right circular cylinder that fits in a sphere of radius 1.**
### Diagram Explanation:
The diagram shows a sphere with a larger black circle representing its boundary. Inside the sphere is a magenta-colored right circular cylinder inscribed within.
- **h:** The height of the cylinder, shown as a vertical line parallel to the sides of the cylinder.
- **r:** The radius of the cylinder's base, depicted on the top circle inside the cylinder.
- **R:** The radius of the sphere, with a value of 1, shown as a blue line extending from the center of the sphere to the edge of the sphere.
The diagram illustrates the relationship between the cylinder and the sphere in which it is inscribed.
### Objective:
Calculate the volume (V) of this cylinder, considering the constraint that it fits perfectly within the sphere. The volume is represented by the formula:
\[ V = \text{___} \]
You need to fill in this blank with the calculated volume of the cylinder based on the given conditions.
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