The figure shows a rubber cuboid that measures 114 m by 36 m by 36 m.
- Find the maximum number of 5-m cubes that can be cut from the rubber cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 114 ÷ 5
= 22 r 4
Breath = Height
Number of cubes along the breadth or height
= 36 ÷ 5
= 7 r 1
Maximum number of 5 m cubes
= 22 x 7 x 7
= 1078
(b)
Area of the 2 squares
= 2 x 36 x 36
= 2592 m
2 Area of the top and bottom bases
= 2 x 114 x 36
= 8208 m
2 Area of 1 L-shaped side
= 114 x 1 + (36 - 1) x 4
= 114 + 140
= 254 m
2Area of 2 L-shaped sides
= 2 x 254
= 508 m
2 Total surface area
= 8208 + 2592 + 508
= 11308 m
2 Answer(s): (a) 1078; (b) 11308 m
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