Question

Find the surface area of a closed rectangular box with a length, breadth and height of 6cm, 5cm and 3cm, respectively.

Answer 1

To find the total surface area of a rectangular solid, we need to calculate the sum of all its sides. Since the question mentions that it is a closed surface, the total number of sides will be 6. Two opposite surfaces that are equal in area.

Complete step by step solution:

The area of surface labelled “1”,
$6 \times 3 = 18\;c{m^2}$

The area of surface labelled “2”,
$6 \times 5 = 30\;c{m^2}$

The area of surface labelled “3”,
$5 \times 3 = 15\;c{m^2}$

We know that there are two of each type of surface in a closed rectangular box.

Therefore, the total surface area = 2[ Area (Surface1) + Area (Surface2) + Area (Surface3)] unit$^2$ Putting the values in the above written formula,

Total surface area of the box$= 2 \times [18 + 30 + 15]$ cm$^2$ $= 2 \times 63$cm$^2$=126
cm$^2$

Note: Since the question has mentioned that the box is closed, the number of surfaces to be counted in order to calculate the total surface area is 6. For an open rectangular box the number of surfaces will be 5. Whenever there is a “tank” mentioned in the question, the number of surfaces becomes 5. When there are problems that revolve around the dimensions of a room that is to be painted, consider the total surface area of 4 sides of a room, unless the roof or floor are specifically mentioned.