A student has some cubes that are all the same size - OCR - GCSE Maths - Question 10 - 2021 - Paper 3
Question 10
A student has some cubes that are all the same size.
Each cube is 3 cm by 3 cm by 3 cm.
They put 4 of these cubes together to make this shape.
Calculate the surfac... show full transcript
Worked Solution & Example Answer:A student has some cubes that are all the same size - OCR - GCSE Maths - Question 10 - 2021 - Paper 3
Step 1
Calculate the surface area of one cube
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Answer
The surface area of a cube is calculated using the formula:
extSurfaceArea=6imesa2
where ( a ) is the length of a side of the cube.
For one cube with side length 3 cm:
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Answer
When the four cubes are put together, some faces are hidden, which means we cannot simply add the surface areas of the individual cubes. We need to determine how many faces are exposed.
Considering the shape made by 4 cubes (as shown in the image), the arrangement typically reveals:
3 faces for each of the two cubes stacked vertically
5 faces for the two cubes on the bottom (not counting the base face)
Hence, the total exposed faces need to be calculated.
Step 3
Calculate total exposed surface area
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Answer
There are effectively 10 faces exposed:
Each of the 2 cubes in the middle contributes 3 faces.
Each of the bottom cubes contributes 5 faces.
Therefore, the total surface area of the entire shape is:
