What Is The Total Surface Area Of A Cube With A Side Length Of 5 Cm?A) 150 Cm 2 150 \, \text{cm}^2 150 Cm 2 B) 125 Cm 2 125 \, \text{cm}^2 125 Cm 2 C) 100 Cm 2 100 \, \text{cm}^2 100 Cm 2 D) 200 Cm 2 200 \, \text{cm}^2 200 Cm 2

Mar 10, 2025 by ADMIN 228 views

**Calculating the Total Surface Area of a Cube: A Step-by-Step Guide**

===========================================================

Introduction

In geometry, a cube is a three-dimensional solid object with six square faces, each of which is a rectangle with all sides of equal length. The total surface area of a cube is the sum of the areas of all its faces. In this article, we will explore how to calculate the total surface area of a cube with a given side length.

Understanding the Formula

The formula for calculating the total surface area of a cube is:

Total Surface Area = 6 × (side length)^2

This formula is derived from the fact that a cube has six square faces, each with an area equal to the square of the side length. By multiplying the area of one face by 6, we get the total surface area of the cube.

Calculating the Total Surface Area of a Cube with a Side Length of 5 cm

Now, let's apply the formula to calculate the total surface area of a cube with a side length of 5 cm.

Step 1: Square the side length

To calculate the area of one face, we need to square the side length. In this case, the side length is 5 cm.

5 cm × 5 cm = 25 cm^2

Step 2: Multiply the area by 6

Now, we multiply the area of one face by 6 to get the total surface area.

6 × 25 cm^2 = 150 cm^2

Therefore, the total surface area of a cube with a side length of 5 cm is 150 cm^2.

Conclusion

In conclusion, calculating the total surface area of a cube is a straightforward process that involves squaring the side length and multiplying the result by 6. By applying this formula, we can easily calculate the total surface area of a cube with a given side length.

Comparison of Options

Now, let's compare our result with the given options:

A) $150 \, \text{cm}^2$
B) $125 \, \text{cm}^2$
C) $100 \, \text{cm}^2$
D) $200 \, \text{cm}^2$

Our result matches option A) $150 \, \text{cm}^2$ .

Real-World Applications

Calculating the total surface area of a cube has many real-world applications, such as:

Architecture: Architects use the formula to calculate the surface area of buildings, bridges, and other structures.
Engineering: Engineers use the formula to calculate the surface area of machines, vehicles, and other equipment.
Science: Scientists use the formula to calculate the surface area of molecules, cells, and other biological structures.

Tips and Tricks

Here are some tips and tricks to help you calculate the total surface area of a cube:

Use the formula: The formula is a simple and efficient way to calculate the total surface area of a cube.
Check your units: Make sure to use the correct units, such as cm^2 or m^2.
Double-check your calculations: Double-check your calculations to ensure accuracy.

Frequently Asked Questions

Here are some frequently asked questions about calculating the total surface area of a cube:

Q: What is the formula for calculating the total surface area of a cube? A: The formula is: Total Surface Area = 6 × (side length)^2
Q: How do I calculate the total surface area of a cube with a side length of 10 cm? A: To calculate the total surface area, square the side length (10 cm × 10 cm = 100 cm^2) and multiply the result by 6 (6 × 100 cm^2 = 600 cm^2).
Q: What is the total surface area of a cube with a side length of 5 cm? A: The total surface area of a cube with a side length of 5 cm is 150 cm^2.

====================================================================

Introduction

In our previous article, we explored how to calculate the total surface area of a cube using the formula: Total Surface Area = 6 × (side length)^2. In this article, we will answer some frequently asked questions about calculating the total surface area of a cube.

Q: What is the formula for calculating the total surface area of a cube?

A: The formula for calculating the total surface area of a cube is:

Total Surface Area = 6 × (side length)^2

This formula is derived from the fact that a cube has six square faces, each with an area equal to the square of the side length.

Q: How do I calculate the total surface area of a cube with a side length of 10 cm?

A: To calculate the total surface area of a cube with a side length of 10 cm, follow these steps:

Square the side length: 10 cm × 10 cm = 100 cm^2
Multiply the area by 6: 6 × 100 cm^2 = 600 cm^2

Therefore, the total surface area of a cube with a side length of 10 cm is 600 cm^2.

Q: What is the total surface area of a cube with a side length of 5 cm?

A: The total surface area of a cube with a side length of 5 cm is 150 cm^2. To calculate this, follow these steps:

Square the side length: 5 cm × 5 cm = 25 cm^2
Multiply the area by 6: 6 × 25 cm^2 = 150 cm^2

Q: How do I calculate the total surface area of a cube with a side length of 0.5 m?

A: To calculate the total surface area of a cube with a side length of 0.5 m, follow these steps:

Square the side length: 0.5 m × 0.5 m = 0.25 m^2
Multiply the area by 6: 6 × 0.25 m^2 = 1.5 m^2

Therefore, the total surface area of a cube with a side length of 0.5 m is 1.5 m^2.

Q: What is the total surface area of a cube with a side length of 2 mm?

A: The total surface area of a cube with a side length of 2 mm is 24 mm^2. To calculate this, follow these steps:

Square the side length: 2 mm × 2 mm = 4 mm^2
Multiply the area by 6: 6 × 4 mm^2 = 24 mm^2

Q: How do I calculate the total surface area of a cube with a side length of 10 mm?

A: To calculate the total surface area of a cube with a side length of 10 mm, follow these steps:

Square the side length: 10 mm × 10 mm = 100 mm^2
Multiply the area by 6: 6 × 100 mm^2 = 600 mm^2

Therefore, the total surface area of a cube with a side length of 10 mm is 600 mm^2.

Q: What is the total surface area of a cube with a side length of 1 cm?

A: The total surface area of a cube with a side length of 1 cm is 6 cm^2. To calculate this, follow these steps:

Square the side length: 1 cm × 1 cm = 1 cm^2
Multiply the area by 6: 6 × 1 cm^2 = 6 cm^2