KJSEA 2025 Maths Q38 — Net and Surface Area of a Cuboid
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The Question
“Karen modelled a cuboid with dimensions 5 cm by 3 cm by 2 cm. (a) Draw the net of the cuboid. (b) Using the net, find the total surface area of the cuboid.”
Understand the shape and its faces
A cuboid is a closed box, so it has six flat rectangular faces that meet in pairs. Each pair of opposite faces is identical. With sides of 5 cm, 3 cm and 2 cm, the three different rectangles you can make are 5 by 3, 5 by 2 and 3 by 2. Knowing these three pairs tells you everything you need before you draw or add anything.
Draw the net by unfolding the box
Imagine cutting along some edges and opening the box out flat. Put the four side faces in a row so they wrap around the middle: the front and back are the 5 by 2 rectangles, and the two ends are the 3 by 2 rectangles. Then attach the top and bottom as flaps, each a 5 by 3 rectangle. Check that every one of the six faces appears exactly once and none is missing or repeated.
Front and back are 5 by 2, the two ends are 3 by 2, and the top and bottom flaps are 5 by 3.
Find the area of each pair of faces
The area of a rectangle is length times width. Work out the area of one face from each pair, then remember that its opposite partner has the same area. So you get 15 square centimetres for a 5 by 3 face, 10 for a 5 by 2 face, and 6 for a 3 by 2 face.
Add the areas of all six faces
Because the faces come in matching pairs, add the three different areas and then double the total. This is faster than adding six separate numbers and it uses the fact that opposite faces are equal. Doubling 31 square centimetres gives the full outer area of the box.
Final Result
The total surface area of the cuboid is 62 square centimetres.
Why this method works
The total surface area is just the amount of flat material needed to cover the whole box, which is exactly what the net shows once it is opened out. Because a cuboid has three pairs of identical opposite faces, you only need to work out three areas and double their sum instead of measuring all six separately. This is why the formula 2 times length by width plus length by height plus width by height works, and here it collapses neatly to 2 times 31.
Add the six faces one by one: 15 + 15 + 10 + 10 + 6 + 6 = 62 square centimetres, which matches.