The figure shows a metallic cuboid that measures 131 m by 29 m by 29 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
= 131 ÷ 7
= 18 r 5
Breath = Height
Number of cubes along the breadth or height
= 29 ÷ 7
= 4 r 1
Maximum number of 7 m cubes
= 18 x 4 x 4
= 288
(b)
Area of the 2 squares
= 2 x 29 x 29
= 1682 m
2 Area of the top and bottom bases
= 2 x 131 x 29
= 7598 m
2 Area of 1 L-shaped side
= 131 x 1 + (29 - 1) x 5
= 131 + 140
= 271 m
2Area of 2 L-shaped sides
= 2 x 271
= 542 m
2 Total surface area
= 7598 + 1682 + 542
= 9822 m
2 Answer(s): (a) 288; (b) 9822 m
2