The figure shows a rubber cuboid that measures 137 cm by 45 cm by 45 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
= 137 ÷ 8
= 17 r 1
Breath = Height
Number of cubes along the breadth or height
= 45 ÷ 8
= 5 r 5
Maximum number of 8 cm cubes
= 17 x 5 x 5
= 425
(b)
Area of the 2 squares
= 2 x 45 x 45
= 4050 cm
2 Area of the top and bottom bases
= 2 x 137 x 45
= 12330 cm
2 Area of 1 L-shaped side
= 137 x 5 + (45 - 5) x 1
= 685 + 40
= 725 cm
2Area of 2 L-shaped sides
= 2 x 725
= 1450 cm
2 Total surface area
= 12330 + 4050 + 1450
= 17830 cm
2 Answer(s): (a) 425; (b) 17830 cm
2