By what scale factor is the volume of the cylinder below affected when the radius and height are multiplied by a scale factor of 3? Use the figure below to help you answer the question by figuring its volume AND the volume of the other described cylinder. Compare the two values and find the volume scale factor. 3 4
By what scale factor is the volume of the cylinder below affected when the radius and height are multiplied by a scale factor of 3? Use the figure below to help you answer the question by figuring its volume AND the volume of the other described cylinder. Compare the two values and find the volume scale factor. 3 4
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![By what scale factor is the volume of the cylinder below affected when the radius and height are multiplied by a scale factor of 3? Use the figure below to help you answer the question by figuring its volume AND the volume of the other described cylinder. Compare the two values and find the volume scale factor.
The diagram shows a cylinder with a radius of 3 units and a height of 4 units.
To solve this:
1. Calculate the volume of the original cylinder:
\[
V = \pi r^2 h = \pi (3)^2 (4) = 36\pi
\]
2. Calculate the volume of the scaled cylinder (with both dimensions multiplied by 3):
\[
\text{New radius} = 3 \times 3 = 9
\]
\[
\text{New height} = 4 \times 3 = 12
\]
\[
V_{\text{new}} = \pi (9)^2 (12) = 972\pi
\]
3. Compare the two volumes:
\[
\text{Volume scale factor} = \frac{V_{\text{new}}}{V} = \frac{972\pi}{36\pi} = 27
\]
Thus, the volume scale factor is 27.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2df48705-4238-4207-b57b-19ed7b40517e%2Fd95a5741-13be-4729-92b4-3ab85a768183%2Fwge14b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:By what scale factor is the volume of the cylinder below affected when the radius and height are multiplied by a scale factor of 3? Use the figure below to help you answer the question by figuring its volume AND the volume of the other described cylinder. Compare the two values and find the volume scale factor.
The diagram shows a cylinder with a radius of 3 units and a height of 4 units.
To solve this:
1. Calculate the volume of the original cylinder:
\[
V = \pi r^2 h = \pi (3)^2 (4) = 36\pi
\]
2. Calculate the volume of the scaled cylinder (with both dimensions multiplied by 3):
\[
\text{New radius} = 3 \times 3 = 9
\]
\[
\text{New height} = 4 \times 3 = 12
\]
\[
V_{\text{new}} = \pi (9)^2 (12) = 972\pi
\]
3. Compare the two volumes:
\[
\text{Volume scale factor} = \frac{V_{\text{new}}}{V} = \frac{972\pi}{36\pi} = 27
\]
Thus, the volume scale factor is 27.
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