Formula for Total Surface Area of a Cuboid

Oct 13, 2025 by pynkocean.com 1 views

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Introduction

In geometry, a cuboid is a three-dimensional solid object with six rectangular faces. It is also known as a rectangular prism. The total surface area of a cuboid is the sum of the areas of all its faces. In this article, we will learn how to find the total surface area of a solid cuboid given its volume, width, length, and breadth.

Formula for Total Surface Area of a Cuboid

The formula for the total surface area of a cuboid is:

TSA = 2(lb + bh + hl)

where TSA is the total surface area, l is the length, b is the breadth, and h is the height (or width) of the cuboid.

Given Values

We are given the following values:

Volume (V) = 480 cm³
Width (w) = 12 cm
Length (l) = 8 cm
Breadth (b) = 6 cm (Note: The breadth is not given in the problem, but we can calculate it using the formula for the volume of a cuboid: V = lwh)

Calculating the Breadth

Using the formula for the volume of a cuboid, we can calculate the breadth as follows:

V = lwh 480 = 8 × w × 6 w = 480 / (8 × 6) w = 10 cm

Calculating the Total Surface Area

Now that we have the values of length, breadth, and width, we can calculate the total surface area using the formula:

TSA = 2(lb + bh + hl) = 2(8 × 10 + 10 × 12 + 12 × 8) = 2(80 + 120 + 96) = 2 × 296 = 592 cm²

Conclusion

In this article, we learned how to find the total surface area of a solid cuboid given its volume, width, length, and breadth. We used the formula for the total surface area of a cuboid and calculated the breadth using the formula for the volume of a cuboid. The total surface area of the cuboid is 592 cm².

Formula for Volume of a Cuboid

The formula for the volume of a cuboid is:

V = lwh

where V is the volume, l is the length, w is the width, and h is the height (or breadth) of the cuboid.

Formula for Total Surface Area of a Cuboid

The formula for the total surface area of a cuboid is:

TSA = 2(lb + bh + hl)

where TSA is the total surface area, l is the length, b is the breadth, and h is the height (or width) of the cuboid.

Real-World Applications

The total surface area of a cuboid has many real-world applications, such as:

Calculating the surface area of a building or a room
Calculating the surface area of a container or a box
Calculating the surface area of a solid object in engineering and architecture

Tips and Tricks

When calculating the total surface area of a cuboid, make sure to use the correct formula and values.
When calculating the breadth of a cuboid, use the formula for the volume of a cuboid.
When calculating the total surface area of a cuboid, use the formula TSA = 2(lb + bh + hl).

Common Mistakes

Using the wrong formula for the total surface area of a cuboid
Using the wrong values for the length, breadth, and width of the cuboid
Not calculating the breadth of the cuboid using the formula for the volume of a cuboid

Conclusion

In conclusion, the total surface area of a solid cuboid is an important concept in geometry and has many real-world applications. By using the correct formula and values, we can calculate the total surface area of a cuboid. Remember to use the formula TSA = 2(lb + bh + hl) and calculate the breadth using the formula for the volume of a cuboid.

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Introduction

In our previous article, we learned how to find the total surface area of a solid cuboid given its volume, width, length, and breadth. In this article, we will answer some frequently asked questions related to the total surface area of a cuboid.

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

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

TSA = 2(lb + bh + hl)

where TSA is the total surface area, l is the length, b is the breadth, and h is the height (or width) of the cuboid.

Q: How do I calculate the breadth of a cuboid?

A: To calculate the breadth of a cuboid, you can use the formula for the volume of a cuboid:

V = lwh

where V is the volume, l is the length, w is the width, and h is the height (or breadth) of the cuboid.

Q: What are the real-world applications of the total surface area of a cuboid?

A: The total surface area of a cuboid has many real-world applications, such as:

Calculating the surface area of a building or a room
Calculating the surface area of a container or a box
Calculating the surface area of a solid object in engineering and architecture

Q: What are some common mistakes to avoid when calculating the total surface area of a cuboid?

A: Some common mistakes to avoid when calculating the total surface area of a cuboid include:

Using the wrong formula for the total surface area of a cuboid
Using the wrong values for the length, breadth, and width of the cuboid
Not calculating the breadth of the cuboid using the formula for the volume of a cuboid

Q: How do I calculate the total surface area of a cuboid with a non-rectangular base?

A: To calculate the total surface area of a cuboid with a non-rectangular base, you will need to use a different formula. The formula for the total surface area of a cuboid with a non-rectangular base is:

TSA = 2(lb + bh + hl) + 2(lw + lh + wh)

where TSA is the total surface area, l is the length, b is the breadth, and h is the height (or width) of the cuboid.

Q: Can I use the formula for the total surface area of a cuboid to calculate the surface area of a sphere?

A: No, you cannot use the formula for the total surface area of a cuboid to calculate the surface area of a sphere. The formula for the surface area of a sphere is:

SA = 4πr²

where SA is the surface area and r is the radius of the sphere.

Q: How do I calculate the total surface area of a cuboid with a curved surface?

A: To calculate the total surface area of a cuboid with a curved surface, you will need to use a different formula. The formula for the total surface area of a cuboid with a curved surface is:

TSA = 2(lb + bh + hl) + 2πrh

where TSA is the total surface area, l is the length, b is the breadth, h is the height (or width) of the cuboid, and r is the radius of the curved surface.

Q: Can I use the formula for the total surface area of a cuboid to calculate the surface area of a cylinder?

A: No, you cannot use the formula for the total surface area of a cuboid to calculate the surface area of a cylinder. The formula for the surface area of a cylinder is:

SA = 2πrh + 2πr²

where SA is the surface area, r is the radius, and h is the height of the cylinder.