A Cylinder Has A Diameter Of 40 Feet And A Height Of 32 Feet. What Is The Surface Area Of The Cylinder? Express The Answer In Terms Of $\pi$.Recall The Formula $S_A = 2 \pi R^2 + 2 \pi R H$.

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Introduction

When it comes to calculating the surface area of a cylinder, many of us may feel a sense of unease. The formula $S_A = 2 \pi r^2 + 2 \pi r h$ can seem daunting, especially when dealing with large numbers. However, with a step-by-step approach and a clear understanding of the formula, we can unravel the mystery of $\pi$ and find the surface area of the cylinder.

Understanding the Formula

The formula for the surface area of a cylinder is given by $S_A = 2 \pi r^2 + 2 \pi r h$. Here, $r$ represents the radius of the cylinder, and $h$ represents the height of the cylinder. To find the surface area, we need to substitute the given values of $r$ and $h$ into the formula.

Given Values

We are given that the diameter of the cylinder is 40 feet. Since the diameter is twice the radius, we can find the radius by dividing the diameter by 2.

diameter = 40
radius = diameter / 2
print(radius)

The radius of the cylinder is 20 feet. We are also given that the height of the cylinder is 32 feet.

Substituting Values into the Formula

Now that we have the values of $r$ and $h$, we can substitute them into the formula for the surface area.

import math

radius = 20
height = 32

surface_area = 2 * math.pi * (radius ** 2) + 2 * math.pi * radius * height
print(surface_area)

Expressing the Answer in Terms of $\pi$

The surface area of the cylinder is given by the expression $1600\pi + 1280\pi$. We can simplify this expression by combining like terms.

import math

surface_area = 1600 * math.pi + 1280 * math.pi
simplified_surface_area = (1600 + 1280) * math.pi
print(simplified_surface_area)

The simplified expression for the surface area of the cylinder is $2880\pi$.

Conclusion

In conclusion, we have unraveled the mystery of $\pi$ and found the surface area of the cylinder. By substituting the given values of $r$ and $h$ into the formula for the surface area, we were able to express the answer in terms of $\pi$. The surface area of the cylinder is $2880\pi$.

Frequently Asked Questions

• What is the formula for the surface area of a cylinder?
  • The formula for the surface area of a cylinder is given by $S_A = 2 \pi r^2 + 2 \pi r h$.
• How do I find the surface area of a cylinder?
  • To find the surface area of a cylinder, you need to substitute the given values of $r$ and $h$ into the formula.
• Can I express the answer in terms of $\pi$?
  • Yes, you can express the answer in terms of $\pi$ by simplifying the expression.

Step-by-Step Solution

1. Find the radius of the cylinder by dividing the diameter by 2.
2. Substitute the values of $r$ and $h$ into the formula for the surface area.
3. Simplify the expression by combining like terms.
4. Express the answer in terms of $\pi$.

Real-World Applications

The surface area of a cylinder has many real-world applications, including:

• Calculating the surface area of a tank or a container.
• Finding the surface area of a pipe or a tube.
• Determining the surface area of a cylinder-shaped object.

Final Thoughts

In conclusion, the surface area of a cylinder is an important concept in mathematics. By understanding the formula and how to apply it, we can solve problems and find the surface area of a cylinder. The surface area of the cylinder is $2880\pi$.

Introduction

In our previous article, we unraveled the mystery of $\pi$ and found the surface area of a cylinder. However, we know that there are many more questions that need to be answered. In this article, we will provide a comprehensive Q&A section to help you understand the concept of the surface area of a cylinder.

Q&A

Q1: What is the formula for the surface area of a cylinder?

A1: The formula for the surface area of a cylinder is given by $S_A = 2 \pi r^2 + 2 \pi r h$.

Q2: How do I find the surface area of a cylinder?

A2: To find the surface area of a cylinder, you need to substitute the given values of $r$ and $h$ into the formula.

Q3: Can I express the answer in terms of $\pi$?

A3: Yes, you can express the answer in terms of $\pi$ by simplifying the expression.

Q4: What is the radius of the cylinder?

A4: The radius of the cylinder is half of the diameter. If the diameter is 40 feet, then the radius is 20 feet.

Q5: How do I calculate the surface area of a cylinder with a diameter of 50 feet and a height of 30 feet?

A5: To calculate the surface area of a cylinder with a diameter of 50 feet and a height of 30 feet, you need to substitute the values of $r$ and $h$ into the formula. The radius is 25 feet, and the height is 30 feet.

import math

radius = 25
height = 30

surface_area = 2 * math.pi * (radius ** 2) + 2 * math.pi * radius * height
print(surface_area)

Q6: Can I use the formula for the surface area of a cylinder to find the surface area of a sphere?

A6: No, the formula for the surface area of a cylinder is not applicable to a sphere. The formula for the surface area of a sphere is given by $S_A = 4 \pi r^2$.

Q7: How do I find the surface area of a cylinder with a radius of 15 feet and a height of 20 feet?

A7: To find the surface area of a cylinder with a radius of 15 feet and a height of 20 feet, you need to substitute the values of $r$ and $h$ into the formula.

import math

radius = 15
height = 20

surface_area = 2 * math.pi * (radius ** 2) + 2 * math.pi * radius * height
print(surface_area)

Q8: Can I use the formula for the surface area of a cylinder to find the surface area of a cone?

A8: No, the formula for the surface area of a cylinder is not applicable to a cone. The formula for the surface area of a cone is given by $S_A = \pi r^2 + \pi r l$, where $l$ is the slant height of the cone.

Q9: How do I find the surface area of a cylinder with a diameter of 60 feet and a height of 40 feet?

A9: To find the surface area of a cylinder with a diameter of 60 feet and a height of 40 feet, you need to substitute the values of $r$ and $h$ into the formula. The radius is 30 feet, and the height is 40 feet.

import math

radius = 30
height = 40

surface_area = 2 * math.pi * (radius ** 2) + 2 * math.pi * radius * height
print(surface_area)

Q10: Can I use the formula for the surface area of a cylinder to find the surface area of a rectangular prism?

A10: No, the formula for the surface area of a cylinder is not applicable to a rectangular prism. The formula for the surface area of a rectangular prism is given by $S_A = 2lw + 2lh + 2wh$, where $l$, $w$, and $h$ are the length, width, and height of the prism, respectively.

Conclusion

In conclusion, we have provided a comprehensive Q&A section to help you understand the concept of the surface area of a cylinder. We have answered questions on how to find the surface area of a cylinder, how to express the answer in terms of $\pi$, and how to calculate the surface area of a cylinder with different dimensions. We hope that this Q&A section has been helpful in clarifying any doubts you may have had on the subject.