The figure shows a wooden cuboid that measures 142 cm by 38 cm by 38 cm.
- Find the maximum number of 9-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
= 142 ÷ 9
= 15 r 7
Breath = Height
Number of cubes along the breadth or height
= 38 ÷ 9
= 4 r 2
Maximum number of 9 cm cubes
= 15 x 4 x 4
= 240
(b)
Area of the 2 squares
= 2 x 38 x 38
= 2888 cm
2 Area of the top and bottom bases
= 2 x 142 x 38
= 10792 cm
2 Area of 1 L-shaped side
= 142 x 2 + (38 - 2) x 7
= 284 + 252
= 536 cm
2Area of 2 L-shaped sides
= 2 x 536
= 1072 cm
2 Total surface area
= 10792 + 2888 + 1072
= 14752 cm
2 Answer(s): (a) 240; (b) 14752 cm
2