Question

Find the total surface area of the following cuboid:

Answer 1

Hint: In the given question, we have been given that there is a cuboid with given length, breadth and height. We have to calculate the total surface area of it. This question can be easily calculated if we know the formula of total surface area of the cuboid. It must be kept in mind that total surface area and lateral surface area have different formulae and must not be confused with one another. There is only one major difference between the two surface areas.

Formula Used:
We are going to use the formula of total surface area of cuboid, which is:
\[TSA = 2\left( {lb + bh + lh} \right)\] square units

Complete step-by-step answer:
In the given question,
\[l = 6cm\]
\[b = 4cm\]
\[h = 2cm\]
There is just one simple difference between total surface area (total surface area is also written as surface area) and lateral surface area – the areas of the roof and the ceiling are excluded in the lateral surface area.
Now, applying the formula of total surface area, \[TSA = 2\left( {lb + bh + lh} \right)\], we get,
\[TSA = 2\left( {6 \times 4 + 4 \times 2 + 6 \times 2} \right) = 2\left( {44} \right) = 88{\rm{ c}}{{\rm{m}}^2}\]
Hence, the total surface area of the given cuboid is \[88{\rm{ }}c{m^2}\].

Note:Here it was given that we had to find the total surface area, so we applied the formula for the same. It does not matter if we jumble up the measurements’ product which is multiplied in the formula because all of the three measurements’ products, taken two at a time, are finally being added only. In the question, if they would have been asking for lateral surface area, then we would have needed to apply a different formula.