A spherical snowball is melting. Find the approximate change in volume if the radius decreases from 4 cm to 3.5 cm. If the radius decreases from 4 cm to 3.5 cm, the change in volume will be cm. (Round to the nearest tenth as needed.)
A spherical snowball is melting. Find the approximate change in volume if the radius decreases from 4 cm to 3.5 cm. If the radius decreases from 4 cm to 3.5 cm, the change in volume will be cm. (Round to the nearest tenth as needed.)
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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![**Problem Statement:**
A spherical snowball is melting. Find the approximate change in volume if the radius decreases from 4 cm to 3.5 cm.
**Question:**
If the radius decreases from 4 cm to 3.5 cm, the change in volume will be ______ cm³.
(Round to the nearest tenth as needed.)
**Explanation:**
In this problem, you need to calculate the change in volume of a sphere as its radius decreases. The formula for the volume \( V \) of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
Where:
- \( V \) is the volume,
- \( r \) is the radius of the sphere,
- \( \pi \) is approximately 3.14159.
To find the change in volume:
1. Calculate the volume with an initial radius of 4 cm.
2. Calculate the volume with a decreased radius of 3.5 cm.
3. Subtract the final volume from the initial volume to find the change.
Remember to round your answer to the nearest tenth.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fff3158bb-c7a6-4ac4-bdef-e27086080d78%2F3aee0644-60f6-422a-9de2-58614b620523%2Ftfjov9b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A spherical snowball is melting. Find the approximate change in volume if the radius decreases from 4 cm to 3.5 cm.
**Question:**
If the radius decreases from 4 cm to 3.5 cm, the change in volume will be ______ cm³.
(Round to the nearest tenth as needed.)
**Explanation:**
In this problem, you need to calculate the change in volume of a sphere as its radius decreases. The formula for the volume \( V \) of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
Where:
- \( V \) is the volume,
- \( r \) is the radius of the sphere,
- \( \pi \) is approximately 3.14159.
To find the change in volume:
1. Calculate the volume with an initial radius of 4 cm.
2. Calculate the volume with a decreased radius of 3.5 cm.
3. Subtract the final volume from the initial volume to find the change.
Remember to round your answer to the nearest tenth.
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