30) A

The wooden puzzle itself is a cube.

The surface of the cube is made up of 3cm cubes and 1cm cubes.

Length of 1 side of puzzle = 3 + 3 + 1 + 1 = 8cm

Volume = 8 x 8 x 8 = 512 cm³

There are 8 cubes with side 3cm.

Volume = 8 x 3 x 3 x 3 = 8 x 27 = 216 cm³

Number of 1cm cubes which are adjacent to two sides = 24

Volume = 1 x 1 x 1 x 24 = 24 cm³

Number of extra 1 cm cubes on each side = 20

Number of sides = 6

Number of extra 1 cm cubes = 6 x 20 = 120

Volume = 120 x 1 x 1 x 1 = 120cm³

Volume taken by 1cm and 3cm cubes = 120 + 24 + 216 = 360 cm³

The remaining volume must be covered by the 2cm cubes.

Remaining volume = 512 – 360 = 152cm³

Volume of one 2cm cube = 2 x 2 x 2 = 8cm³

Number of 2cm cubes = 152 ÷ 8 = 19 cubes

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