Use this surface area of a cuboid calculator a mathematical tool designed to compute the total area of all faces of a cuboid (also known as a rectangular prism).
A cuboid is a three-dimensional geometric shape with six rectangular faces. It’s characterized by its length (l), width (w), and height (h). The surface area calculator takes these three measurements as input and calculates the total surface area.
For example, let’s consider a cuboid with the following dimensions:
- Length (l) = 10 cm
- Width (w) = 5 cm
- Height (h) = 3 cm
Surface Area of a Cuboid Calculator
| Length | Width | Height | Surface Area | Conversion (if applicable) |
|---|---|---|---|---|
| 10 cm | 6 cm | 4 cm | 248 cm² | 0.0248 m² (1 m² = 10000 cm²) |
| 2.5 m | 1.8 m | 3 m | 35.1 m² | 351000 cm² (1 m² = 10000 cm²) |
| 15 in | 9 in | 7 in | 726 in² | 5.0417 ft² (1 ft² = 144 in²) |
| 4 ft | 3 ft | 2.5 ft | 71 ft² | 6.5968 m² (1 m² ≈ 10.7639 ft²) |
| 1.2 m | 0.8 m | 0.5 m | 3.32 m² | 33200 cm² (1 m² = 10000 cm²) |
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Surface Area Of A Cuboid Calculation Formula
The formula for calculating the surface area of a cuboid is:
Surface Area = 2(lw + lh + wh)
Where:
- l = length
- w = width
- h = height
This formula accounts for all six faces of the cuboid:
- Two faces with area l × w (top and bottom)
- Two faces with area l × h (front and back)
- Two faces with area w × h (left and right sides)
Consider a cuboid with dimensions:
- Length (l) = 8 m
- Width (w) = 4 m
- Height (h) = 3 m
Applying the formula:
- Calculate lw: 8 × 4 = 32
- Calculate lh: 8 × 3 = 24
- Calculate wh: 4 × 3 = 12
- Sum these products: 32 + 24 + 12 = 68
- Multiply by 2: 68 × 2 = 136
The surface area of this cuboid is 136 square meters (m²).
How to find the surface area of a cuboid
To find the surface area of a cuboid, follow these steps:
- Measure the dimensions: Determine the length, width, and height of the cuboid using a consistent unit of measurement.
- Apply the formula: Use the formula Surface Area = 2(lw + lh + wh).
- Calculate each component:
- Multiply length by width (lw)
- Multiply length by height (lh)
- Multiply width by height (wh)
- Sum the products: Add the results from step 3.
- Multiply by 2: Double the sum to account for all six faces.
- Review the result: The final number represents the total surface area in square units.
What is the total surface area of a cuboid
The total surface area of a cuboid is the sum of the areas of all six rectangular faces. It represents the entire outer “skin” of the cuboid if it were to be unfolded and laid flat.
The total surface area includes:
- The area of the top and bottom faces (2 × length × width)
- The area of the front and back faces (2 × length × height)
- The area of the left and right side faces (2 × width × height)
This comprehensive measurement is crucial in various real-world applications, such as:
- Determining the amount of paint needed to cover a box
- Calculating the material required for packaging
- Estimating heat loss or gain through the walls of a room
What is the surface area of the cuboid 3 5 2?
Let’s calculate the surface area of a cuboid with dimensions 3, 5, and 2 units:
- Length (l) = 5 units
- Width (w) = 3 units
- Height (h) = 2 units
Using the formula Surface Area = 2(lw + lh + wh):
- Calculate lw: 5 × 3 = 15
- Calculate lh: 5 × 2 = 10
- Calculate wh: 3 × 2 = 6
- Sum these products: 15 + 10 + 6 = 31
- Multiply by 2: 31 × 2 = 62
The surface area of the cuboid 3 5 2 is 62 square units.
Surface Area Of A Cuboid Conversion Table
| Original Dimensions | Converted Dimensions | Surface Area | Conversion Equation |
|---|---|---|---|
| 5 ft × 3 ft × 2 ft | 1.524 m × 0.914 m × 0.610 m | 4.65 m² | 1 ft = 0.3048 m |
| 20 in × 15 in × 10 in | 50.8 cm × 38.1 cm × 25.4 cm | 7,742.0 cm² | 1 in = 2.54 cm |
| 1 yd × 2 yd × 1.5 yd | 0.914 m × 1.829 m × 1.372 m | 10.97 m² | 1 yd = 0.9144 m |
| 100 cm × 50 cm × 30 cm | 1 m × 0.5 m × 0.3 m | 1.9 m² | 1 cm = 0.01 m |
