The figure shows a plastic cuboid that measures 101 m by 29 m by 29 m.
- Find the maximum number of 3-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 ÷ 3
= 33 r 2
Breath = Height
Number of cubes along the breadth or height
= 29 ÷ 3
= 9 r 2
Maximum number of 3 m cubes
= 33 x 9 x 9
= 2673
(b)
Area of the 2 squares
= 2 x 29 x 29
= 1682 m
2 Area of the top and bottom bases
= 2 x 101 x 29
= 5858 m
2 Area of 1 L-shaped side
= 101 x 2 + (29 - 2) x 2
= 202 + 54
= 256 m
2Area of 2 L-shaped sides
= 2 x 256
= 512 m
2 Total surface area
= 5858 + 1682 + 512
= 8052 m
2 Answer(s): (a) 2673; (b) 8052 m
2