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
![**Problem Statement:**
A ball of radius 15 has a round hole of radius 8 drilled through its center. Find the volume of the resulting solid.
**Given Answer:**
\[
\frac{11452\pi}{3}
\]
**Analysis:**
This problem involves calculating the volume of a sphere with a cylindrical hole drilled through its center. The sphere has a radius of 15, and the hole (cylinder) has a radius of 8.
**Explanation of the Answer:**
The answer provided, \(\frac{11452\pi}{3}\), is marked incorrect, indicating either a miscalculation or misunderstanding of the volume calculation.
To find the correct volume of the resulting solid:
1. Calculate the volume of the sphere using \( V_{\text{sphere}} = \frac{4}{3} \pi r^3\).
2. Calculate the volume of the cylinder using \( V_{\text{cylinder}} = \pi r_{\text{cylinder}}^2 h\), where \( h \) is the height of the cylinder, equal to twice the sphere's radius (since it goes through the center).
3. Subtract the cylinder’s volume from the sphere’s volume to find the volume of the resulting solid.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3aff424b-0e96-4e90-b1d6-dc40303839e0%2F924a4c9d-4f62-4b35-b743-62784ce2f114%2Fi5hmz6p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
A ball of radius 15 has a round hole of radius 8 drilled through its center. Find the volume of the resulting solid.
**Given Answer:**
\[
\frac{11452\pi}{3}
\]
**Analysis:**
This problem involves calculating the volume of a sphere with a cylindrical hole drilled through its center. The sphere has a radius of 15, and the hole (cylinder) has a radius of 8.
**Explanation of the Answer:**
The answer provided, \(\frac{11452\pi}{3}\), is marked incorrect, indicating either a miscalculation or misunderstanding of the volume calculation.
To find the correct volume of the resulting solid:
1. Calculate the volume of the sphere using \( V_{\text{sphere}} = \frac{4}{3} \pi r^3\).
2. Calculate the volume of the cylinder using \( V_{\text{cylinder}} = \pi r_{\text{cylinder}}^2 h\), where \( h \) is the height of the cylinder, equal to twice the sphere's radius (since it goes through the center).
3. Subtract the cylinder’s volume from the sphere’s volume to find the volume of the resulting solid.
Expert Solution
Step 1: Given that variables are
Step by step
Solved in 3 steps with 3 images
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
Can you show me how to get the right answer in the picture?
Transcribed Image Text:**Problem Description:**
A ball of radius 15 has a round hole of radius 8 drilled through its center. Find the volume of the resulting solid.
---
**Input:**
The submitted answer is "21" with an indication that it is incorrect.
**Correct Solution:**
The correct volume of the resulting solid is provided as "8557.1160795713."
Solution
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