The figure shows a rubber cuboid that measures 121 cm by 40 cm by 40 cm.
- Find the maximum number of 7-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
= 121 ÷ 7
= 17 r 2
Breath = Height
Number of cubes along the breadth or height
= 40 ÷ 7
= 5 r 5
Maximum number of 7 cm cubes
= 17 x 5 x 5
= 425
(b)
Area of the 2 squares
= 2 x 40 x 40
= 3200 cm
2 Area of the top and bottom bases
= 2 x 121 x 40
= 9680 cm
2 Area of 1 L-shaped side
= 121 x 5 + (40 - 5) x 2
= 605 + 70
= 675 cm
2Area of 2 L-shaped sides
= 2 x 675
= 1350 cm
2 Total surface area
= 9680 + 3200 + 1350
= 14230 cm
2 Answer(s): (a) 425; (b) 14230 cm
2