..... The volume is multiplied by (Type an integer or a simplified fraction.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
8)
![**Understanding the Effect of Radius Changes on Sphere Volume**
**Question:**
What happens to the volume of a sphere if its radius is multiplied by 6?
**Explanation:**
The volume of the sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
If the radius \( r \) is multiplied by a factor of 6, the new volume \( V' \) is:
\[ V' = \frac{4}{3} \pi (6r)^3 \]
\[ V' = \frac{4}{3} \pi (216r^3) \]
\[ V' = 216 \left( \frac{4}{3} \pi r^3 \right) \]
This shows that the volume of the sphere is multiplied by 216.
**Answer:**
The volume is multiplied by 216.
**User Instruction:**
(Type an integer or a simplified fraction.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8cc1e18c-4006-463a-a6de-c3009c3618f2%2F4de1ebd6-ed32-4286-937c-94a905de0ba5%2F06cz3tm_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding the Effect of Radius Changes on Sphere Volume**
**Question:**
What happens to the volume of a sphere if its radius is multiplied by 6?
**Explanation:**
The volume of the sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
If the radius \( r \) is multiplied by a factor of 6, the new volume \( V' \) is:
\[ V' = \frac{4}{3} \pi (6r)^3 \]
\[ V' = \frac{4}{3} \pi (216r^3) \]
\[ V' = 216 \left( \frac{4}{3} \pi r^3 \right) \]
This shows that the volume of the sphere is multiplied by 216.
**Answer:**
The volume is multiplied by 216.
**User Instruction:**
(Type an integer or a simplified fraction.)
Expert Solution
Step 1
Given
New radius=6r
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