Calculate the total surface area of a cupboard which measures 12cm by 10cm by 8cm

Analysis

The question asks for the total surface area of a cupboard. Since the cupboard has three different dimensions (length, width, and height), it is a rectangular prism (or cuboid).

Concept

The total surface area ($A$) of a cuboid is the sum of the areas of all its six faces. A cuboid has three pairs of identical faces. The formula is:

Where:

• $l$ = length
• $b$ = breadth (width)
• $h$ = height

Solution

Given the dimensions:

• $l = 12\text{ cm}$
• $b = 10\text{ cm}$
• $h = 8\text{ cm}$

Step 1: Calculate the area of each pair of faces.

• $l \times b = 12 \times 10 = 120\text{ cm}^2$
• $l \times h = 12 \times 8 = 96\text{ cm}^2$
• $b \times h = 10 \times 8 = 80\text{ cm}^2$

Step 2: Sum these areas and multiply by 2.

• Sum $= 120 + 96 + 80 = 296\text{ cm}^2$
• Total Surface Area $= 2 \times 296 = 592\text{ cm}^2$

Conclusion

Comparing our result to the given options, the correct value is $592\text{ cm}^2$. This matches option B.

Exam Tip

When calculating the surface area of a cuboid, a common mistake is to forget to multiply by 2 or to miss one of the three pairs of sides. Always remember that a box has a top/bottom, front/back, and left/right side—that is why we sum three products and multiply the result by two!