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

Understand the Problem

The question is asking for the formula to calculate the surface area of a cuboid. A cuboid is a three-dimensional shape with six rectangular faces, and the surface area can be calculated by adding the areas of all the faces together. The formula is typically expressed as 2(lb + bh + hl), where l is the length, b is the breadth, and h is the height of the cuboid.

Answer

The surface area of a cuboid is given by the formula $SA = 2(lb + bh + hl)$.
Answer for screen readers

The formula to calculate the surface area of a cuboid is

$$ SA = 2(lb + bh + hl) $$

Steps to Solve

  1. Identify the dimensions of the cuboid

To calculate the surface area, we need the values for the length ($l$), breadth ($b$), and height ($h$) of the cuboid.

  1. Apply the surface area formula

Using the formula for the surface area of a cuboid:

$$ SA = 2(lb + bh + hl) $$

where $SA$ is the surface area, $l$ is the length, $b$ is the breadth, and $h$ is the height.

  1. Calculate the individual areas of each pair of faces

We can break down the components:

  • The area of the two length-breadth faces: $2(lb)$
  • The area of the two breadth-height faces: $2(bh)$
  • The area of the two height-length faces: $2(hl)$

So, when summed together, we end up with:

$$ SA = 2(lb + bh + hl) $$

  1. Substitute the values into the formula

Once we have the values for $l$, $b$, and $h$, we replace them in the formula to compute the total surface area.

The formula to calculate the surface area of a cuboid is

$$ SA = 2(lb + bh + hl) $$

More Information

The surface area represents the total area of all six rectangular faces of a cuboid. Understanding this formula helps in various practical applications, such as packaging and construction, where knowing the surface area is essential for material estimation.

Tips

  • Forgetting to multiply by 2: Many people forget to include the factor of 2 that accounts for both sets of opposite faces. Always remember that the surface area includes two of each rectangular face area.
  • Incorrectly identifying dimensions: Mistakes can occur if the dimensions are not clearly labeled. Ensure you know which measurement corresponds to length, breadth, and height.
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