The figure shows a plastic cuboid that measures 101 m by 14 m by 14 m.
- Find the maximum number of 8-m 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
= 101 ÷ 8
= 12 r 5
Breath = Height
Number of cubes along the breadth or height
= 14 ÷ 8
= 1 r 6
Maximum number of 8 m cubes
= 12 x 1 x 1
= 12
(b)
Area of the 2 squares
= 2 x 14 x 14
= 392 m
2 Area of the top and bottom bases
= 2 x 101 x 14
= 2828 m
2 Area of 1 L-shaped side
= 101 x 6 + (14 - 6) x 5
= 606 + 40
= 646 m
2Area of 2 L-shaped sides
= 2 x 646
= 1292 m
2 Total surface area
= 2828 + 392 + 1292
= 4512 m
2 Answer(s): (a) 12; (b) 4512 m
2