The figure shows a plastic cuboid that measures 104 m by 15 m by 15 m.
- Find the maximum number of 7-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
= 104 ÷ 7
= 14 r 6
Breath = Height
Number of cubes along the breadth or height
= 15 ÷ 7
= 2 r 1
Maximum number of 7 m cubes
= 14 x 2 x 2
= 56
(b)
Area of the 2 squares
= 2 x 15 x 15
= 450 m
2 Area of the top and bottom bases
= 2 x 104 x 15
= 3120 m
2 Area of 1 L-shaped side
= 104 x 1 + (15 - 1) x 6
= 104 + 84
= 188 m
2Area of 2 L-shaped sides
= 2 x 188
= 376 m
2 Total surface area
= 3120 + 450 + 376
= 3946 m
2 Answer(s): (a) 56; (b) 3946 m
2