The figure shows a rubber cuboid that measures 114 cm by 24 cm by 24 cm.
- Find the maximum number of 9-cm cubes that can be cut from the rubber cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 114 ÷ 9
= 12 r 6
Breath = Height
Number of cubes along the breadth or height
= 24 ÷ 9
= 2 r 6
Maximum number of 9 cm cubes
= 12 x 2 x 2
= 48
(b)
Area of the 2 squares
= 2 x 24 x 24
= 1152 cm
2 Area of the top and bottom bases
= 2 x 114 x 24
= 5472 cm
2 Area of 1 L-shaped side
= 114 x 6 + (24 - 6) x 6
= 684 + 108
= 792 cm
2Area of 2 L-shaped sides
= 2 x 792
= 1584 cm
2 Total surface area
= 5472 + 1152 + 1584
= 8208 cm
2 Answer(s): (a) 48; (b) 8208 cm
2 
