Perimeter of a Face of a Cube

Oct 13, 2025 by miodeya.com 20 views

Introduction

In this problem, we are given a cube with an edge length of 9 centimeters. We are asked to find out how much larger the perimeter of a face of the new cube is when the side length is increased by a factor of 3. To solve this problem, we need to understand the concept of perimeter and how it changes when the side length of a cube is increased.

Perimeter of a Face of a Cube

The perimeter of a face of a cube is the distance around the face of the cube. Since a cube has six faces, each face has a perimeter that is equal to the sum of the lengths of its four edges. If we denote the edge length of the cube as 's', then the perimeter of a face of the cube is given by:

P = 4s

Increasing the Side Length by a Factor of 3

Now, let's consider what happens when the side length of the cube is increased by a factor of 3. If the original edge length is 9 centimeters, then the new edge length will be 3 times 9, which is 27 centimeters.

Calculating the Perimeter of a Face of the New Cube

To find the perimeter of a face of the new cube, we can use the formula:

P = 4s

where s is the new edge length, which is 27 centimeters. Plugging in the value of s, we get:

P = 4(27) P = 108 cm

Comparing the Perimeters of the Original and New Cubes

Now, let's compare the perimeters of the original and new cubes. The original cube has a perimeter of:

P = 4(9) P = 36 cm

The new cube has a perimeter of:

P = 108 cm

To find out how much larger the perimeter of the new cube is, we can subtract the perimeter of the original cube from the perimeter of the new cube:

108 cm - 36 cm = 72 cm

Conclusion

In conclusion, when the side length of a cube is increased by a factor of 3, the perimeter of a face of the new cube is 72 cm larger than the perimeter of a face of the original cube.

Answer

The correct answer is A. 72 cm.

Additional Information

It's worth noting that the question asks for the difference in perimeter, not the new perimeter itself. Therefore, the correct answer is 72 cm, not 108 cm.

Mathematical Formulas and Equations

Perimeter of a face of a cube: P = 4s
New edge length: s = 3(9) = 27 cm
Perimeter of a face of the new cube: P = 4(27) = 108 cm
Difference in perimeter: 108 cm - 36 cm = 72 cm
A Cube Has an Edge Length of 9 Centimeters: Q&A =====================================================

Introduction

In our previous article, we discussed how to calculate the perimeter of a face of a cube when the side length is increased by a factor of 3. In this article, we will answer some frequently asked questions related to the problem.

Q: What is the perimeter of a face of the original cube?

A: The perimeter of a face of the original cube is 36 cm. This can be calculated using the formula P = 4s, where s is the edge length of the cube, which is 9 cm.

Q: What is the perimeter of a face of the new cube?

A: The perimeter of a face of the new cube is 108 cm. This can be calculated using the formula P = 4s, where s is the new edge length, which is 27 cm.

Q: How much larger is the perimeter of a face of the new cube compared to the original cube?

A: The perimeter of a face of the new cube is 72 cm larger than the perimeter of a face of the original cube. This can be calculated by subtracting the perimeter of the original cube from the perimeter of the new cube: 108 cm - 36 cm = 72 cm.

Q: What happens to the volume of the cube when the side length is increased by a factor of 3?

A: When the side length of the cube is increased by a factor of 3, the volume of the cube increases by a factor of 3^3, which is 27. This is because the volume of a cube is given by V = s^3, where s is the edge length of the cube.

Q: How does the surface area of the cube change when the side length is increased by a factor of 3?

A: When the side length of the cube is increased by a factor of 3, the surface area of the cube increases by a factor of 3^2, which is 9. This is because the surface area of a cube is given by A = 6s^2, where s is the edge length of the cube.

Q: Can I use the same formula to calculate the perimeter of a face of a cube with a different edge length?

A: Yes, you can use the same formula P = 4s to calculate the perimeter of a face of a cube with a different edge length. Simply plug in the value of the edge length into the formula to get the perimeter.

Q: What if I want to find the perimeter of a face of a cube with a fractional edge length?

A: You can still use the formula P = 4s to calculate the perimeter of a face of a cube with a fractional edge length. However, you will need to perform the calculation carefully to avoid any errors.

Conclusion

In conclusion, we have answered some frequently asked questions related to the problem of calculating the perimeter of a face of a cube when the side length is increased by a factor of 3. We hope that this article has been helpful in clarifying any doubts you may have had.

Additional Resources

Cube Perimeter Calculator: A online calculator that can be used to calculate the perimeter of a face of a cube.
Cube Volume Calculator: A online calculator that can be used to calculate the volume of a cube.
Cube Surface Area Calculator: A online calculator that can be used to calculate the surface area of a cube.