Shu Xin had a rectangular block measuring 32 cm by 12 cm by 24 cm. She painted all the faces of the block. Then, she cut the block into 2-cm cubes.

(a)
How many 2-cm cubes did Shu Xin cut from the block?
(b)
How many of these 2-cm cubes had none of the faces painted?

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Worked solution

12(a)

1. Find the number of 2-cm cubes along the length, width, and height.

Number of cubes along length = $32 \div 2 = 16$
Number of cubes along width = $12 \div 2 = 6$
Number of cubes along height = $24 \div 2 = 12$

2. Calculate the total number of cubes.

Total number of cubes = $16 \times 6 \times 12 = 1152$

Answer

$2304$

12(b)

1. Find the number of 2-cm cubes along each dimension of the unpainted inner block

Number of cubes along the length $= (32 \div 2) - 2 = 16 - 2 = 14$
Number of cubes along the width $= (12 \div 2) - 2 = 6 - 2 = 4$
Number of cubes along the height $= (24 \div 2) - 2 = 12 - 2 = 10$

2. Calculate the total number of unpainted cubes

Number of unpainted cubes $= 14 \times 4 \times 10 = 560$

Answer

$560$

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Shu Xin had a rectangular block measuring 32 cm by 12 cm by 24 cm. She painted all the faces of the block. Then, she cut the block into 2-cm cubes.

Worked solution

12(a)

12(b)

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