The figure shows a wooden cuboid that measures 107 cm by 16 cm by 16 cm.
- Find the maximum number of 6-cm cubes that can be cut from the wooden cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 107 ÷ 6
= 17 r 5
Breath = Height
Number of cubes along the breadth or height
= 16 ÷ 6
= 2 r 4
Maximum number of 6 cm cubes
= 17 x 2 x 2
= 68
(b)
Area of the 2 squares
= 2 x 16 x 16
= 512 cm
2 Area of the top and bottom bases
= 2 x 107 x 16
= 3424 cm
2 Area of 1 L-shaped side
= 107 x 4 + (16 - 4) x 5
= 428 + 60
= 488 cm
2Area of 2 L-shaped sides
= 2 x 488
= 976 cm
2 Total surface area
= 3424 + 512 + 976
= 4912 cm
2 Answer(s): (a) 68; (b) 4912 cm
2