What is the surface area of a right circular cylinder whose base's diameter is 6.52, and height is 15.19? Jse л= 3.14 as needed. Round to two decimal places as needed.
What is the surface area of a right circular cylinder whose base's diameter is 6.52, and height is 15.19? Jse л= 3.14 as needed. Round to two decimal places as needed.
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter62: Volumes Of Prisms And Cylinders
Section: Chapter Questions
Problem 38A: A copper casting is in the shape of a prism with an equilateral triangle base. The length of each...
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![### Cylinder Surface Area Problem
**Question:**
What is the surface area of a right circular cylinder whose base's diameter is 16.52, and height is 15.19?
*Use π = 3.14 as needed. Round to two decimal places as needed.*
**Explanation:**
To find the surface area of a right circular cylinder, you can use the formula:
\[ \text{Surface Area} = 2\pi r (r + h) \]
where \( r \) is the radius of the base, and \( h \) is the height of the cylinder.
Given:
- Diameter \( d = 16.52 \)
- Height \( h = 15.19 \)
- \( \pi = 3.14 \)
First, find the radius \( r \):
\[ r = \frac{d}{2} = \frac{16.52}{2} = 8.26 \]
Now, plug the values into the surface area formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 8.26 \times (8.26 + 15.19) \]
Calculate the inner term:
\[ 8.26 + 15.19 = 23.45 \]
Now, substitute back into the formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 8.26 \times 23.45 \]
Performing the multiplication:
\[ \text{Surface Area} \approx 2 \times 3.14 \times 8.26 \times 23.45 \]
\[ \text{Surface Area} \approx 1219.04 \]
Therefore, the surface area of the cylinder, rounded to two decimal places, is approximately \( 1219.04 \) square units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F91652952-972c-437d-817e-6a9e046f1c10%2F366516c5-c806-4116-9b07-f7e472d17353%2Fjezykcp_processed.png&w=3840&q=75)
Transcribed Image Text:### Cylinder Surface Area Problem
**Question:**
What is the surface area of a right circular cylinder whose base's diameter is 16.52, and height is 15.19?
*Use π = 3.14 as needed. Round to two decimal places as needed.*
**Explanation:**
To find the surface area of a right circular cylinder, you can use the formula:
\[ \text{Surface Area} = 2\pi r (r + h) \]
where \( r \) is the radius of the base, and \( h \) is the height of the cylinder.
Given:
- Diameter \( d = 16.52 \)
- Height \( h = 15.19 \)
- \( \pi = 3.14 \)
First, find the radius \( r \):
\[ r = \frac{d}{2} = \frac{16.52}{2} = 8.26 \]
Now, plug the values into the surface area formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 8.26 \times (8.26 + 15.19) \]
Calculate the inner term:
\[ 8.26 + 15.19 = 23.45 \]
Now, substitute back into the formula:
\[ \text{Surface Area} = 2 \times 3.14 \times 8.26 \times 23.45 \]
Performing the multiplication:
\[ \text{Surface Area} \approx 2 \times 3.14 \times 8.26 \times 23.45 \]
\[ \text{Surface Area} \approx 1219.04 \]
Therefore, the surface area of the cylinder, rounded to two decimal places, is approximately \( 1219.04 \) square units.
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