The Dimensions of a Cuboid

Oct 13, 2025 by talynt.org 39 views

Introduction

In this article, we will explore the dimensions of a cuboid and the cost of digging a pit. We will start by finding the dimensions of a cuboid with a total surface area of 88 m², given that its dimensions are in the ratio 1:2:3. Then, we will calculate the cost of digging a cuboidal pit 6 m long, 4 m broad, and 3 m deep at the rate of *250.

The Dimensions of a Cuboid

A cuboid is a three-dimensional solid object with six rectangular faces. The dimensions of a cuboid are its length, width, and height. Given that the dimensions of the cuboid are in the ratio 1:2:3, we can let the length be x, the width be 2x, and the height be 3x.

The total surface area of a cuboid is given by the formula:

2(lw + lh + wh)

where l is the length, w is the width, and h is the height.

Substituting the values of l, w, and h in terms of x, we get:

2(x(2x) + x(3x) + 2x(3x))

Simplifying the expression, we get:

2(2x² + 3x² + 6x²)

Combine like terms:

2(11x²)

The total surface area is given as 88 m², so we can set up the equation:

2(11x²) = 88

Divide both sides by 2:

11x² = 44

Divide both sides by 11:

x² = 4

Take the square root of both sides:

x = 2

Now that we have found the value of x, we can find the dimensions of the cuboid:

Length (l) = x = 2 m Width (w) = 2x = 4 m Height (h) = 3x = 6 m

The Cost of Digging a Pit

The cost of digging a pit is given by the formula:

Cost = Volume of the pit × Rate

The volume of a cuboid is given by the formula:

Volume = lwh

where l is the length, w is the width, and h is the height.

Substituting the values of l, w, and h, we get:

Volume = (6 m)(4 m)(3 m)

Multiply the values:

Volume = 72 m³

The rate of digging is given as *250, so we can set up the equation:

Cost = 72 m³ × *250

Multiply the values:

Cost = *18000

Conclusion

In this article, we found the dimensions of a cuboid with a total surface area of 88 m², given that its dimensions are in the ratio 1:2:3. We also calculated the cost of digging a cuboidal pit 6 m long, 4 m broad, and 3 m deep at the rate of *250.

The Formulae Used

The total surface area of a cuboid is given by the formula: 2(lw + lh + wh)
The volume of a cuboid is given by the formula: Volume = lwh
The cost of digging a pit is given by the formula: Cost = Volume of the pit × Rate

The Key Terms Used

Cuboid: A three-dimensional solid object with six rectangular faces.
Dimensions: The length, width, and height of a cuboid.
Total surface area: The sum of the areas of all the faces of a cuboid.
Volume: The amount of space inside a cuboid.
Rate: The cost of digging a pit per unit volume.

The Applications of the Formulae

The formulae for the total surface area and volume of a cuboid can be used to find the dimensions of a cuboid given its total surface area or volume.
The formula for the cost of digging a pit can be used to find the cost of digging a pit given its volume and rate.

The Limitations of the Formulae

The formulae for the total surface area and volume of a cuboid assume that the cuboid has six rectangular faces.
The formula for the cost of digging a pit assumes that the rate of digging is constant.

The Future Scope of the Formulae

The formulae for the total surface area and volume of a cuboid can be used to find the dimensions of a cuboid given its total surface area or volume in different shapes and sizes.
The formula for the cost of digging a pit can be used to find the cost of digging a pit given its volume and rate in different materials and conditions.
The Dimensions of a Cuboid and the Cost of Digging a Pit: Q&A ===========================================================

Introduction

In our previous article, we explored the dimensions of a cuboid and the cost of digging a pit. We found the dimensions of a cuboid with a total surface area of 88 m², given that its dimensions are in the ratio 1:2:3. We also calculated the cost of digging a cuboidal pit 6 m long, 4 m broad, and 3 m deep at the rate of *250.

In this article, we will answer some of the most frequently asked questions related to the dimensions of a cuboid and the cost of digging a pit.

Q&A

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 2(lw + lh + wh), where l is the length, w is the width, and h is the height.

Q: What is the formula for the volume of a cuboid?

A: The formula for the volume of a cuboid is lwh, where l is the length, w is the width, and h is the height.

Q: How do I find the dimensions of a cuboid given its total surface area?

A: To find the dimensions of a cuboid given its total surface area, you can use the formula 2(lw + lh + wh) = total surface area. Then, you can solve for l, w, and h.

Q: How do I find the cost of digging a pit given its volume and rate?

A: To find the cost of digging a pit given its volume and rate, you can use the formula Cost = Volume × Rate.

Q: What is the rate of digging a pit?

A: The rate of digging a pit is the cost of digging a pit per unit volume. It is usually expressed in units such as *250 per cubic meter.

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

A: To calculate the volume of a cuboid, you can use the formula lwh, where l is the length, w is the width, and h is the height.

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

A: The total surface area of a cuboid is the sum of the areas of all its faces.

Q: How do I find the dimensions of a cuboid given its volume?

A: To find the dimensions of a cuboid given its volume, you can use the formula lwh = volume. Then, you can solve for l, w, and h.

Q: What is the cost of digging a pit?

A: The cost of digging a pit is the amount of money required to dig a pit of a given volume.

Q: How do I calculate the cost of digging a pit?

A: To calculate the cost of digging a pit, you can use the formula Cost = Volume × Rate.