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 $SA = 2\pi R^2 + 2\pi Rh$.A. $1,320 \pi \text{ Ft}^2$B.

Introduction

In mathematics, the surface area of a cylinder is a fundamental concept that is used to calculate the total area of the surface of the cylinder. The surface area of a cylinder is given by the formula SA = 2πr^2 + 2πrh, where r is the radius of the base of the cylinder and h is the height of the cylinder. In this article, we will use this formula to calculate the surface area of a cylinder with a diameter of 40 feet and a height of 32 feet.

Understanding the Formula

The formula for the surface area of a cylinder is SA = 2πr^2 + 2πrh. This formula consists of two parts: the first part, 2πr^2, represents the area of the two circular bases of the cylinder, and the second part, 2πrh, represents the area of the curved surface of the cylinder.

Calculating the Radius

To calculate the surface area of the cylinder, we need to find the radius of the base of the cylinder. The diameter of the cylinder is given as 40 feet, so the radius is half of the diameter, which is 20 feet.

Calculating the Surface Area

Now that we have the radius, we can calculate the surface area of the cylinder using the formula SA = 2πr^2 + 2πrh. Plugging in the values, we get:

SA = 2π(20)^2 + 2π(20)(32) SA = 2π(400) + 2π(640) SA = 800π + 1280π SA = 2080π

Conclusion

In this article, we calculated the surface area of a cylinder with a diameter of 40 feet and a height of 32 feet. Using the formula SA = 2πr^2 + 2πrh, we found that the surface area of the cylinder is 2080π square feet.

Recap

• The surface area of a cylinder is given by the formula SA = 2πr^2 + 2πrh.
• The radius of the base of the cylinder is half of the diameter.
• The surface area of the cylinder consists of the area of the two circular bases and the area of the curved surface.

Example Problems

1. A cylinder has a diameter of 30 feet and a height of 25 feet. What is the surface area of the cylinder?
2. A cylinder has a radius of 15 feet and a height of 30 feet. What is the surface area of the cylinder?

Answer Key

1. 2100π square feet
2. 1800π square feet

Discussion

The surface area of a cylinder is an important concept in mathematics that has many real-world applications. In this article, we calculated the surface area of a cylinder with a diameter of 40 feet and a height of 32 feet. We also provided example problems and an answer key to help readers practice calculating the surface area of a cylinder.

References

• "Mathematics for Dummies" by Mark Ryan
• "Calculus for Dummies" by Mark Ryan
• "Geometry for Dummies" by Mark Ryan

Related Articles

• Calculating the Volume of a Cylinder
• Calculating the Surface Area of a Sphere
• Calculating the Surface Area of a Cone
  Q&A: Surface Area of a Cylinder =====================================

Frequently Asked Questions

In this article, we will answer some of the most frequently asked questions about the surface area of a cylinder.

Q: What is the surface area of a cylinder?

A: The surface area of a cylinder is the total area of the surface of the cylinder. It consists of the area of the two circular bases and the area of the curved surface.

Q: How do I calculate the surface area of a cylinder?

A: To calculate the surface area of a cylinder, you need to use the formula SA = 2πr^2 + 2πrh, where r is the radius of the base of the cylinder and h is the height of the cylinder.

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

A: The formula for the surface area of a cylinder is SA = 2πr^2 + 2πrh.

Q: What is the radius of the base of a cylinder?

A: The radius of the base of a cylinder is half of the diameter.

Q: How do I find the diameter of a cylinder?

A: To find the diameter of a cylinder, you need to measure the distance across the circular base of the cylinder.

Q: What is the height of a cylinder?

A: The height of a cylinder is the distance between the two circular bases.

Q: How do I calculate the surface area of a cylinder with a diameter of 40 feet and a height of 32 feet?

A: To calculate the surface area of a cylinder with a diameter of 40 feet and a height of 32 feet, you need to use the formula SA = 2πr^2 + 2πrh, where r is the radius of the base of the cylinder and h is the height of the cylinder. Plugging in the values, you get:

SA = 2π(20)^2 + 2π(20)(32) SA = 2π(400) + 2π(640) SA = 800π + 1280π SA = 2080π

Q: What is the surface area of a cylinder with a diameter of 30 feet and a height of 25 feet?

A: To calculate the surface area of a cylinder with a diameter of 30 feet and a height of 25 feet, you need to use the formula SA = 2πr^2 + 2πrh, where r is the radius of the base of the cylinder and h is the height of the cylinder. Plugging in the values, you get:

SA = 2π(15)^2 + 2π(15)(25) SA = 2π(225) + 2π(375) SA = 450π + 750π SA = 1200π

Q: What is the surface area of a cylinder with a radius of 15 feet and a height of 30 feet?

A: To calculate the surface area of a cylinder with a radius of 15 feet and a height of 30 feet, you need to use the formula SA = 2πr^2 + 2πrh, where r is the radius of the base of the cylinder and h is the height of the cylinder. Plugging in the values, you get:

SA = 2π(15)^2 + 2π(15)(30) SA = 2π(225) + 2π(450) SA = 450π + 900π SA = 1350π

Conclusion

In this article, we answered some of the most frequently asked questions about the surface area of a cylinder. We provided formulas and examples to help readers understand how to calculate the surface area of a cylinder.

Recap

• The surface area of a cylinder is the total area of the surface of the cylinder.
• The formula for the surface area of a cylinder is SA = 2πr^2 + 2πrh.
• The radius of the base of a cylinder is half of the diameter.
• The height of a cylinder is the distance between the two circular bases.

Example Problems

1. A cylinder has a diameter of 40 feet and a height of 32 feet. What is the surface area of the cylinder?
2. A cylinder has a diameter of 30 feet and a height of 25 feet. What is the surface area of the cylinder?
3. A cylinder has a radius of 15 feet and a height of 30 feet. What is the surface area of the cylinder?

Answer Key

1. 2080π square feet
2. 1200π square feet
3. 1350π square feet

Discussion

The surface area of a cylinder is an important concept in mathematics that has many real-world applications. In this article, we provided formulas and examples to help readers understand how to calculate the surface area of a cylinder.

References

• "Mathematics for Dummies" by Mark Ryan
• "Calculus for Dummies" by Mark Ryan
• "Geometry for Dummies" by Mark Ryan

Related Articles

• Calculating the Volume of a Cylinder
• Calculating the Surface Area of a Sphere
• Calculating the Surface Area of a Cone