The figure shows a wooden cuboid that measures 118 cm by 36 cm by 36 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
= 118 ÷ 8
= 14 r 6
Breath = Height
Number of cubes along the breadth or height
= 36 ÷ 8
= 4 r 4
Maximum number of 8 cm cubes
= 14 x 4 x 4
= 224
(b)
Area of the 2 squares
= 2 x 36 x 36
= 2592 cm
2 Area of the top and bottom bases
= 2 x 118 x 36
= 8496 cm
2 Area of 1 L-shaped side
= 118 x 4 + (36 - 4) x 6
= 472 + 192
= 664 cm
2Area of 2 L-shaped sides
= 2 x 664
= 1328 cm
2 Total surface area
= 8496 + 2592 + 1328
= 12416 cm
2 Answer(s): (a) 224; (b) 12416 cm
2