The figure shows a metallic cuboid that measures 121 m by 50 m by 50 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
= 121 ÷ 8
= 15 r 1
Breath = Height
Number of cubes along the breadth or height
= 50 ÷ 8
= 6 r 2
Maximum number of 8 m cubes
= 15 x 6 x 6
= 540
(b)
Area of the 2 squares
= 2 x 50 x 50
= 5000 m
2 Area of the top and bottom bases
= 2 x 121 x 50
= 12100 m
2 Area of 1 L-shaped side
= 121 x 2 + (50 - 2) x 1
= 242 + 48
= 290 m
2Area of 2 L-shaped sides
= 2 x 290
= 580 m
2 Total surface area
= 12100 + 5000 + 580
= 17680 m
2 Answer(s): (a) 540; (b) 17680 m
2