Mathematics
Junior Kangaroo
2023
12

12

The diagram shows a wooden cube of side 3 cm with a smaller cube of side 1 cm cut out at one corner. A second cube of side 3 cm has a cube of side 1 cm cut out at each corner. How many faces does the shape formed from the second cube have?

A. 6

B. 16

C. 24

D. 30

E. 36

Answer

D. 30

SOLUTIOn

A standard cube has six faces. When a cube is removed from one corner, the number of faces increases by three, as shown in the diagram in the question. Therefore, the cube with a smaller cube cut out at each of its eight corners has a total of (6 + 8 × 3) faces. Therefore the second cube has 30 faces.

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