A Cuboidal Steel Box Is 2m Long 1m Broad And 0.5 M High Find The Cost Of Panting Its Outer Surface At The Rate Of 200 M2

Mar 11, 2025 by ADMIN 121 views

A Cuboidal Steel Box: Calculating the Cost of Painting its Outer Surface

Introduction

When it comes to calculating the cost of painting a cuboidal steel box, we need to consider the surface area of the box that needs to be painted. The surface area of a cuboid is the total area of all its faces, and it can be calculated using the formula: 2(lb + bh + hl), where l, b, and h are the length, breadth, and height of the cuboid, respectively. In this article, we will calculate the surface area of a cuboidal steel box with dimensions 2m long, 1m broad, and 0.5m high, and then use this value to determine the cost of painting its outer surface at a rate of 200 m2.

Calculating the Surface Area of the Cuboidal Steel Box

To calculate the surface area of the cuboidal steel box, we need to use the formula: 2(lb + bh + hl). Plugging in the values of l, b, and h, we get:

2(2 x 1 + 1 x 0.5 + 0.5 x 2) = 2(2 + 0.5 + 1) = 2(3.5) = 7 m2

However, this is the surface area of the box, but we need to consider the fact that the box has six faces, and each face has a different area. To calculate the total surface area, we need to multiply the surface area of one face by 6.

Surface Area of one face = 2m x 1m = 2 m2 Total Surface Area = 6 x 2 m2 = 12 m2

Calculating the Cost of Painting the Outer Surface

Now that we have the total surface area of the cuboidal steel box, we can use this value to determine the cost of painting its outer surface at a rate of 200 m2. To do this, we need to divide the total surface area by the rate per square meter.

Cost of painting = Total Surface Area / Rate per square meter = 12 m2 / 200 m2 = 0.06

However, this is not the final answer, as we need to multiply this value by the cost per square meter to get the total cost.

Cost per square meter = 200 m2 Total Cost = Cost of painting x Cost per square meter = 0.06 x 200 = 12

Conclusion

In this article, we calculated the surface area of a cuboidal steel box with dimensions 2m long, 1m broad, and 0.5m high, and then used this value to determine the cost of painting its outer surface at a rate of 200 m2. We found that the total surface area of the box is 12 m2, and the cost of painting its outer surface is 12.

Calculating the Surface Area of a Cuboid

A cuboid is a three-dimensional solid object with six rectangular faces. The surface area of a cuboid can be calculated using the formula: 2(lb + bh + hl), where l, b, and h are the length, breadth, and height of the cuboid, respectively.

Formula for Surface Area of a Cuboid

The formula for the surface area of a cuboid is:

Surface Area = 2(lb + bh + hl)

Derivation of the Formula

To derive the formula for the surface area of a cuboid, we need to consider the fact that a cuboid has six rectangular faces. Each face has a different area, and we need to calculate the total surface area by adding up the areas of all the faces.

Let's consider a cuboid with dimensions l, b, and h. The surface area of one face is given by:

Surface Area of one face = l x b

Since there are six faces, the total surface area is given by:

Total Surface Area = 6 x (l x b)

However, this is not the final answer, as we need to consider the fact that each face has a different area. To calculate the total surface area, we need to add up the areas of all the faces.

Let's consider the faces of the cuboid:

Face 1: l x b
Face 2: l x h
Face 3: b x h
Face 4: l x b
Face 5: l x h
Face 6: b x h

The total surface area is given by:

Total Surface Area = (l x b) + (l x h) + (b x h) + (l x b) + (l x h) + (b x h) = 2(lb + bh + hl)

This is the final formula for the surface area of a cuboid.

Real-World Applications of Calculating Surface Area

Calculating the surface area of a cuboid has many real-world applications. Some of these applications include:

Architecture: When designing a building, architects need to calculate the surface area of the building to determine the amount of materials needed for construction.
Engineering: Engineers need to calculate the surface area of machines and equipment to determine the amount of materials needed for manufacturing.
Packaging: Companies need to calculate the surface area of packaging materials to determine the amount of materials needed for packaging products.
Art: Artists need to calculate the surface area of canvases and other materials to determine the amount of paint and other materials needed for a project.

Conclusion

Introduction

In our previous article, we calculated the surface area of a cuboidal steel box with dimensions 2m long, 1m broad, and 0.5m high, and then used this value to determine the cost of painting its outer surface at a rate of 200 m2. In this article, we will answer some frequently asked questions related to the surface area of a cuboid and its applications.

Q&A

Q1: What is the formula for the surface area of a cuboid?

A1: The formula for the surface area of a cuboid is: 2(lb + bh + hl), where l, b, and h are the length, breadth, and height of the cuboid, respectively.

Q2: How do I calculate the surface area of a cuboid?

A2: To calculate the surface area of a cuboid, you need to use the formula: 2(lb + bh + hl). Plug in the values of l, b, and h, and then multiply the result by 2.

Q3: What is the difference between the surface area of a cuboid and a rectangle?

A3: The surface area of a cuboid is the total area of all its faces, while the surface area of a rectangle is the area of one face. A cuboid has six faces, while a rectangle has only two faces.

Q4: How do I calculate the cost of painting a cuboid?

A4: To calculate the cost of painting a cuboid, you need to multiply the surface area of the cuboid by the cost per square meter.

Q5: What are some real-world applications of calculating the surface area of a cuboid?

A5: Some real-world applications of calculating the surface area of a cuboid include architecture, engineering, packaging, and art.

Q6: Can I use the formula for the surface area of a cuboid to calculate the surface area of a sphere?

A6: No, the formula for the surface area of a cuboid is not applicable to a sphere. The surface area of a sphere is given by the formula: 4πr^2, where r is the radius of the sphere.

Q7: How do I calculate the surface area of a cuboid with a non-rectangular base?

A7: To calculate the surface area of a cuboid with a non-rectangular base, you need to use the formula: 2(lb + bh + hl), where l, b, and h are the length, breadth, and height of the cuboid, respectively. However, you need to take into account the shape of the base and calculate the area of the base accordingly.

Q8: Can I use the formula for the surface area of a cuboid to calculate the surface area of a cylinder?

A8: No, the formula for the surface area of a cuboid is not applicable to a cylinder. The surface area of a cylinder is given by the formula: 2πrh + 2πr^2, where r is the radius of the cylinder and h is its height.

Q9: How do I calculate the surface area of a cuboid with a curved surface?

A9: To calculate the surface area of a cuboid with a curved surface, you need to use the formula: 2(lb + bh + hl), where l, b, and h are the length, breadth, and height of the cuboid, respectively. However, you need to take into account the shape of the curved surface and calculate the area of the curved surface accordingly.

Q10: Can I use the formula for the surface area of a cuboid to calculate the surface area of a cone?

A10: No, the formula for the surface area of a cuboid is not applicable to a cone. The surface area of a cone is given by the formula: πr^2 + πrl, where r is the radius of the cone and l is its slant height.

Conclusion

In this article, we answered some frequently asked questions related to the surface area of a cuboid and its applications. We hope that this article has provided you with a better understanding of the surface area of a cuboid and its uses in real-world applications.