What is the formula for the surface area of a cuboid?
Understand the Problem
The question is asking for the formula that calculates the surface area of a cuboid, which involves using the dimensions of the cuboid to find the total area of its outer surfaces.
Answer
The surface area formula of a cuboid is given by $SA = 2(lw + lh + wh)$.
Answer for screen readers
The formula for the surface area of a cuboid is: $$ SA = 2(lw + lh + wh) $$
Steps to Solve
- Identify the dimensions of the cuboid
A cuboid has three dimensions: length ($l$), width ($w$), and height ($h$). You'll need to be clear about what these dimensions are.
- Surface Area Formula
The formula for calculating the surface area ($SA$) of a cuboid is given by: $$ SA = 2(lw + lh + wh) $$ This formula accounts for all six faces of the cuboid.
- Calculate Each Component
To apply the formula, calculate each term inside the parentheses:
- Calculate the area of the length and width: $lw$
- Calculate the area of the length and height: $lh$
- Calculate the area of the width and height: $wh$
- Add the Components
Next, sum these area calculations: $$ lw + lh + wh $$
- Multiply the Sum by 2
Finally, multiply the total found in the previous step by 2 to obtain the total surface area: $$ SA = 2(lw + lh + wh) $$
The formula for the surface area of a cuboid is: $$ SA = 2(lw + lh + wh) $$
More Information
The surface area of a cuboid is important in various real-world applications, such as packaging design, construction, and architecture. Understanding how to calculate it helps in determining how much material is needed to cover the cuboid or how much paint is required, among other practical uses.
Tips
- Forgetting to multiply by 2, which would lead to only calculating the area of three faces instead of all six.
- Mixing up the dimensions: ensure you correctly identify which measure corresponds to length, width, or height.
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