Jacque Is Using A Soup Can For A School Project And Wants To Paint It. If The Can Is 13 Cm Tall And Has A Diameter Of 9 Cm, At Least How Many Square Centimeters Of Paint Are Needed? Approximate Using { \pi = 3.14$}$.A. [$826.61 ,

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Introduction

When it comes to creative projects, a little math can go a long way. For Jacque's school project, painting a soup can requires more than just artistic skills – it also demands a basic understanding of geometry. In this article, we'll delve into the world of mathematics and explore how to calculate the surface area of a soup can, ensuring that Jacque has enough paint to bring their vision to life.

Understanding the Problem

To determine the amount of paint needed, we need to calculate the surface area of the soup can. The can is 13 cm tall and has a diameter of 9 cm. We'll use the formula for the surface area of a cylinder, which is given by:

A = 2πrh + 2πr^2

where A is the surface area, π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cylinder.

Calculating the Radius

Before we can plug in the values, we need to find the radius of the base. Since the diameter is given as 9 cm, we can find the radius by dividing the diameter by 2:

r = diameter / 2 = 9 cm / 2 = 4.5 cm

Calculating the Surface Area

Now that we have the radius, we can plug in the values into the formula:

A = 2πrh + 2πr^2 = 2(3.14)(4.5 cm)(13 cm) + 2(3.14)(4.5 cm)^2 = 2(3.14)(58.5 cm^2) + 2(3.14)(20.25 cm^2) = 367.13 cm^2 + 127.14 cm^2 = 494.27 cm^2

However, this is not the total surface area of the can. We also need to consider the area of the two circular ends. To find this, we'll use the formula for the area of a circle:

A = πr^2 = 3.14(4.5 cm)^2 = 3.14(20.25 cm^2) = 63.69 cm^2

Since there are two circular ends, we'll multiply this by 2:

2(63.69 cm^2) = 127.38 cm^2

Now, we'll add this to the surface area of the curved part:

494.27 cm^2 + 127.38 cm^2 = 621.65 cm^2

Conclusion

To ensure that Jacque has enough paint for their school project, we need to calculate the surface area of the soup can. Using the formula for the surface area of a cylinder, we found that the total surface area is approximately 621.65 cm^2. This includes the area of the curved part and the two circular ends. By using this calculation, Jacque can confidently paint their soup can and bring their creative vision to life.

Discussion

  • What other creative projects can you think of that require mathematical calculations?
  • How can you apply the concept of surface area to real-world problems?
  • What are some other formulas or mathematical concepts that you can use to solve problems in art and design?

Additional Resources

Final Answer

Introduction

In our previous article, we explored the concept of surface area and how to calculate it for a soup can. Now, we'll answer some frequently asked questions about this topic to help you better understand the math behind it.

Q: What is the surface area of a soup can?

A: The surface area of a soup can is approximately 621.65 cm^2, which includes the area of the curved part and the two circular ends.

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

A: To calculate the surface area of a soup can, you'll need to use the formula for the surface area of a cylinder:

A = 2πrh + 2πr^2

where A is the surface area, π (pi) is a mathematical constant approximately equal to 3.14, r is the radius of the base, and h is the height of the cylinder.

Q: What is the radius of the base of a soup can?

A: The radius of the base of a soup can is half of the diameter, which is 4.5 cm.

Q: How do I find the height of a soup can?

A: The height of a soup can is given as 13 cm.

Q: What is the formula for the area of a circle?

A: The formula for the area of a circle is:

A = πr^2

where A is the area, π (pi) is a mathematical constant approximately equal to 3.14, and r is the radius of the circle.

Q: Why do I need to consider the area of the two circular ends?

A: You need to consider the area of the two circular ends because they are part of the total surface area of the soup can. The area of the two circular ends is approximately 127.38 cm^2.

Q: Can I use a different value for π?

A: Yes, you can use a different value for π, but keep in mind that the value 3.14 is an approximation. If you use a more precise value for π, your calculation will be more accurate.

Q: What are some real-world applications of surface area?

A: Surface area has many real-world applications, such as:

  • Calculating the amount of paint needed for a project
  • Determining the surface area of a building or a room
  • Calculating the area of a garden or a lawn
  • Determining the surface area of a piece of art or a sculpture

Conclusion

We hope this Q&A article has helped you better understand the concept of surface area and how to calculate it for a soup can. If you have any more questions or need further clarification, feel free to ask.

Additional Resources

Final Answer

The final answer is: 621.65\boxed{621.65}