The volume, V, of a sphere in terms of its radius, r, is given by V (r) = 7³. Express r as a function of V, and find the radius of a sphere with volume of 350 cubic feet. Round your answer for the radius to two decimal places. Enclose numerators and denominators in parentheses. For example, (a - b)/(1+n). Include a multiplication sign between symbols. For example, a * .
The volume, V, of a sphere in terms of its radius, r, is given by V (r) = 7³. Express r as a function of V, and find the radius of a sphere with volume of 350 cubic feet. Round your answer for the radius to two decimal places. Enclose numerators and denominators in parentheses. For example, (a - b)/(1+n). Include a multiplication sign between symbols. For example, a * .
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...
Related questions
Question
![**Volume of a Sphere and Radius Calculation**
The volume, \( V \), of a sphere in terms of its radius, \( r \), is given by the formula:
\[ V(r) = \frac{4}{3} \pi r^3 \]
**Task:**
1. Express \( r \) as a function of \( V \).
2. Find the radius of a sphere with a volume of 350 cubic feet.
**Instructions:**
- Round your answer for the radius to two decimal places.
- Enclose numerators and denominators in parentheses. For example, \( (a - b)/(1 + n) \).
- Include a multiplication sign between symbols. For example, \( a \cdot \pi \).
**Solution Approach:**
1. **Rearrange the formula** to express \( r \) in terms of \( V \).
2. **Calculate the radius** for the given volume.
**Formula:**
\[ r(V) = \left( \frac{3V}{4\pi} \right)^{\frac{1}{3}} \]
For a sphere with a volume of 350 cubic feet, calculate:
\[ r(350) = \left( \frac{3 \times 350}{4\pi} \right)^{\frac{1}{3}} \]
Insert your calculation in the answer box provided.
**Example:**
A sphere with volume 350 cubic feet has a radius of
\[ \text{Number} \]
feet.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7e9c79f-8a95-4aea-89f2-f9a24ba7a1c3%2F50b5279b-b0fb-4e35-97d1-19525758c36c%2F4mgddru_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Volume of a Sphere and Radius Calculation**
The volume, \( V \), of a sphere in terms of its radius, \( r \), is given by the formula:
\[ V(r) = \frac{4}{3} \pi r^3 \]
**Task:**
1. Express \( r \) as a function of \( V \).
2. Find the radius of a sphere with a volume of 350 cubic feet.
**Instructions:**
- Round your answer for the radius to two decimal places.
- Enclose numerators and denominators in parentheses. For example, \( (a - b)/(1 + n) \).
- Include a multiplication sign between symbols. For example, \( a \cdot \pi \).
**Solution Approach:**
1. **Rearrange the formula** to express \( r \) in terms of \( V \).
2. **Calculate the radius** for the given volume.
**Formula:**
\[ r(V) = \left( \frac{3V}{4\pi} \right)^{\frac{1}{3}} \]
For a sphere with a volume of 350 cubic feet, calculate:
\[ r(350) = \left( \frac{3 \times 350}{4\pi} \right)^{\frac{1}{3}} \]
Insert your calculation in the answer box provided.
**Example:**
A sphere with volume 350 cubic feet has a radius of
\[ \text{Number} \]
feet.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 5 images
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning