The figure shows a wooden cuboid that measures 149 cm by 44 cm by 44 cm.
- Find the maximum number of 8-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
= 149 ÷ 8
= 18 r 5
Breath = Height
Number of cubes along the breadth or height
= 44 ÷ 8
= 5 r 4
Maximum number of 8 cm cubes
= 18 x 5 x 5
= 450
(b)
Area of the 2 squares
= 2 x 44 x 44
= 3872 cm
2 Area of the top and bottom bases
= 2 x 149 x 44
= 13112 cm
2 Area of 1 L-shaped side
= 149 x 4 + (44 - 4) x 5
= 596 + 200
= 796 cm
2Area of 2 L-shaped sides
= 2 x 796
= 1592 cm
2 Total surface area
= 13112 + 3872 + 1592
= 18576 cm
2 Answer(s): (a) 450; (b) 18576 cm
2