The figure shows a rubber cuboid that measures 115 cm by 12 cm by 12 cm.
- Find the maximum number of 8-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
= 115 ÷ 8
= 14 r 3
Breath = Height
Number of cubes along the breadth or height
= 12 ÷ 8
= 1 r 4
Maximum number of 8 cm cubes
= 14 x 1 x 1
= 14
(b)
Area of the 2 squares
= 2 x 12 x 12
= 288 cm
2 Area of the top and bottom bases
= 2 x 115 x 12
= 2760 cm
2 Area of 1 L-shaped side
= 115 x 4 + (12 - 4) x 3
= 460 + 24
= 484 cm
2Area of 2 L-shaped sides
= 2 x 484
= 968 cm
2 Total surface area
= 2760 + 288 + 968
= 4016 cm
2 Answer(s): (a) 14; (b) 4016 cm
2