The figure shows a metallic cuboid that measures 144 m by 34 m by 34 m.
- Find the maximum number of 7-m cubes that can be cut from the metallic cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 144 ÷ 7
= 20 r 4
Breath = Height
Number of cubes along the breadth or height
= 34 ÷ 7
= 4 r 6
Maximum number of 7 m cubes
= 20 x 4 x 4
= 320
(b)
Area of the 2 squares
= 2 x 34 x 34
= 2312 m
2 Area of the top and bottom bases
= 2 x 144 x 34
= 9792 m
2 Area of 1 L-shaped side
= 144 x 6 + (34 - 6) x 4
= 864 + 112
= 976 m
2Area of 2 L-shaped sides
= 2 x 976
= 1952 m
2 Total surface area
= 9792 + 2312 + 1952
= 14056 m
2 Answer(s): (a) 320; (b) 14056 m
2