The figure shows a plastic cuboid that measures 136 cm by 33 cm by 33 cm.
- Find the maximum number of 5-cm cubes that can be cut from the plastic cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 136 ÷ 5
= 27 r 1
Breath = Height
Number of cubes along the breadth or height
= 33 ÷ 5
= 6 r 3
Maximum number of 5 cm cubes
= 27 x 6 x 6
= 972
(b)
Area of the 2 squares
= 2 x 33 x 33
= 2178 cm
2 Area of the top and bottom bases
= 2 x 136 x 33
= 8976 cm
2 Area of 1 L-shaped side
= 136 x 3 + (33 - 3) x 1
= 408 + 30
= 438 cm
2Area of 2 L-shaped sides
= 2 x 438
= 876 cm
2 Total surface area
= 8976 + 2178 + 876
= 12030 cm
2 Answer(s): (a) 972; (b) 12030 cm
2