The figure shows a plastic cuboid that measures 139 cm by 32 cm by 32 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
= 139 ÷ 5
= 27 r 4
Breath = Height
Number of cubes along the breadth or height
= 32 ÷ 5
= 6 r 2
Maximum number of 5 cm cubes
= 27 x 6 x 6
= 972
(b)
Area of the 2 squares
= 2 x 32 x 32
= 2048 cm
2 Area of the top and bottom bases
= 2 x 139 x 32
= 8896 cm
2 Area of 1 L-shaped side
= 139 x 2 + (32 - 2) x 4
= 278 + 120
= 398 cm
2Area of 2 L-shaped sides
= 2 x 398
= 796 cm
2 Total surface area
= 8896 + 2048 + 796
= 11740 cm
2 Answer(s): (a) 972; (b) 11740 cm
2