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
- 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.
- 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.
- 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:
$$ SA = 2(lb + bh + hl) $$
- 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.
