The figure shows a metallic cuboid that measures 111 m by 13 m by 13 m.
- Find the maximum number of 6-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
= 111 ÷ 6
= 18 r 3
Breath = Height
Number of cubes along the breadth or height
= 13 ÷ 6
= 2 r 1
Maximum number of 6 m cubes
= 18 x 2 x 2
= 72
(b)
Area of the 2 squares
= 2 x 13 x 13
= 338 m
2 Area of the top and bottom bases
= 2 x 111 x 13
= 2886 m
2 Area of 1 L-shaped side
= 111 x 1 + (13 - 1) x 3
= 111 + 36
= 147 m
2Area of 2 L-shaped sides
= 2 x 147
= 294 m
2 Total surface area
= 2886 + 338 + 294
= 3518 m
2 Answer(s): (a) 72; (b) 3518 m
2