Ahmad's family is packing mooncakes for the Mid-Autumn Festival. Each mooncake box is a cuboid that is 20 cm long, 10 cm wide and 5 cm tall. To make a net for one box, Ahmad must cut out exactly 6 rectangles that will fold into the closed box with no gaps and no overlaps. Which of the following sets of 6 rectangles is the correct net for this box?
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Worked Solution
Step 1: Identify the three pairs of faces on a 20 cm x 10 cm x 5 cm cuboid.
Top and bottom: 20 cm x 10 cm (area = 200 cm2 each)
Front and back: 20 cm x 5 cm (area = 100 cm2 each)
Left and right: 10 cm x 5 cm (area = 50 cm2 each)
Step 2: Count the faces — 2 + 2 + 2 = 6 faces total.
Step 3: Total surface area = 2(200) + 2(100) + 2(50) = 400 + 200 + 100 = 700 cm2.
The set "two 20x10, two 20x5, two 10x5" gives exactly 700 cm2. Check each distractor:
Option B (four 20x10 + two 10x5): SA = 4(200) + 2(50) = 900 cm2 — wrong.
Option C (two 20x10 + four 10x5): SA = 2(200) + 4(50) = 600 cm2 — wrong.
Option D (two 20x10 + four 20x5): SA = 2(200) + 4(100) = 800 cm2 — wrong.
Answer: Two 20 cm x 10 cm rectangles, two 20 cm x 5 cm rectangles and two 10 cm x 5 cm rectangles.
Correct answer: Two 20 cm x 10 cm rectangles, two 20 cm x 5 cm rectangles and two 10 cm x 5 cm rectangles
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