The figure shows a metallic cuboid that measures 139 m by 47 m by 47 m.
- Find the maximum number of 8-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
= 139 ÷ 8
= 17 r 3
Breath = Height
Number of cubes along the breadth or height
= 47 ÷ 8
= 5 r 7
Maximum number of 8 m cubes
= 17 x 5 x 5
= 425
(b)
Area of the 2 squares
= 2 x 47 x 47
= 4418 m
2 Area of the top and bottom bases
= 2 x 139 x 47
= 13066 m
2 Area of 1 L-shaped side
= 139 x 7 + (47 - 7) x 3
= 973 + 120
= 1093 m
2Area of 2 L-shaped sides
= 2 x 1093
= 2186 m
2 Total surface area
= 13066 + 4418 + 2186
= 19670 m
2 Answer(s): (a) 425; (b) 19670 m
2