The gas tank on the back of a tanker truck is shaped as a cylinder. The diameter is 8 feet and the length is 17 feet. What is the surface area and volume of the gas tank?
The gas tank on the back of a tanker truck is shaped as a cylinder. The diameter is 8 feet and the length is 17 feet. What is the surface area and volume of the gas tank?
Chapter5: Exponential And Logarithmic Functions
Section: Chapter Questions
Problem 22PS: In a classroom designed for 30 students, the air conditioning system can move 450 cubic feet of air...
Related questions
Concept explainers
Percentage
A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.
Algebraic Expressions
In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.
Numbers
Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.
Subtraction
Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.
Addition
Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.
Topic Video
Question
Please help/show work .3
![**Calculating the Surface Area and Volume of a Cylindrical Tank**
The gas tank on the back of a tanker truck is shaped as a cylinder. The diameter is 8 feet and the length is 17 feet. What is the surface area and volume of the gas tank?
_Image Description: The image includes a tanker truck with a cylindrical gas tank attached to the back._
To find the **surface area** and **volume** of the cylindrical gas tank, you can use the following mathematical formulas:
**1. Surface Area of a Cylinder:**
The surface area (SA) of a cylinder is calculated using the formula:
\[ SA = 2\pi rh + 2\pi r^2 \]
where:
- \( r \) is the radius of the base of the cylinder
- \( h \) is the height (or length) of the cylinder
- \( \pi \) is approximately 3.14159
Since the diameter of the cylinder is 8 feet, the radius \( r \) will be half of the diameter:
\[ r = \frac{8}{2} = 4 \text{ feet} \]
Now, plug in the values into the surface area formula:
\[ SA = 2\pi (4)(17) + 2\pi (4)^2 \]
\[ SA = 2\pi (68) + 2\pi (16) \]
\[ SA = 136\pi + 32\pi \]
\[ SA = 168\pi \]
When calculated, this approximates to:
\[ SA \approx 168 \times 3.14159 \]
\[ SA \approx 528.16 \text{ square feet} \]
**2. Volume of a Cylinder:**
The volume (V) of a cylinder is calculated using the formula:
\[ V = \pi r^2 h \]
Now, plug in the radius and height into the volume formula:
\[ V = \pi (4)^2 (17) \]
\[ V = \pi (16) (17) \]
\[ V = 272\pi \]
When calculated, this approximates to:
\[ V \approx 272 \times 3.14159 \]
\[ V \approx 854.51 \text{ cubic feet} \]
Therefore, the surface area of the gas tank is approximately 528.16 square feet, and the volume of the gas tank is](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F142e1ae3-c931-47e5-a8d0-830705d30c68%2Fc3b9deb3-4625-4470-820d-b7909345894f%2Fq9c3uk5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Calculating the Surface Area and Volume of a Cylindrical Tank**
The gas tank on the back of a tanker truck is shaped as a cylinder. The diameter is 8 feet and the length is 17 feet. What is the surface area and volume of the gas tank?
_Image Description: The image includes a tanker truck with a cylindrical gas tank attached to the back._
To find the **surface area** and **volume** of the cylindrical gas tank, you can use the following mathematical formulas:
**1. Surface Area of a Cylinder:**
The surface area (SA) of a cylinder is calculated using the formula:
\[ SA = 2\pi rh + 2\pi r^2 \]
where:
- \( r \) is the radius of the base of the cylinder
- \( h \) is the height (or length) of the cylinder
- \( \pi \) is approximately 3.14159
Since the diameter of the cylinder is 8 feet, the radius \( r \) will be half of the diameter:
\[ r = \frac{8}{2} = 4 \text{ feet} \]
Now, plug in the values into the surface area formula:
\[ SA = 2\pi (4)(17) + 2\pi (4)^2 \]
\[ SA = 2\pi (68) + 2\pi (16) \]
\[ SA = 136\pi + 32\pi \]
\[ SA = 168\pi \]
When calculated, this approximates to:
\[ SA \approx 168 \times 3.14159 \]
\[ SA \approx 528.16 \text{ square feet} \]
**2. Volume of a Cylinder:**
The volume (V) of a cylinder is calculated using the formula:
\[ V = \pi r^2 h \]
Now, plug in the radius and height into the volume formula:
\[ V = \pi (4)^2 (17) \]
\[ V = \pi (16) (17) \]
\[ V = 272\pi \]
When calculated, this approximates to:
\[ V \approx 272 \times 3.14159 \]
\[ V \approx 854.51 \text{ cubic feet} \]
Therefore, the surface area of the gas tank is approximately 528.16 square feet, and the volume of the gas tank is
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 1 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.Recommended textbooks for you
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:
9780395977224
Author:
Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:
McDougal Littell