The figure shows a metallic cuboid that measures 137 cm by 46 cm by 46 cm.
- Find the maximum number of 9-cm 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
= 137 ÷ 9
= 15 r 2
Breath = Height
Number of cubes along the breadth or height
= 46 ÷ 9
= 5 r 1
Maximum number of 9 cm cubes
= 15 x 5 x 5
= 375
(b)
Area of the 2 squares
= 2 x 46 x 46
= 4232 cm
2 Area of the top and bottom bases
= 2 x 137 x 46
= 12604 cm
2 Area of 1 L-shaped side
= 137 x 1 + (46 - 1) x 2
= 137 + 90
= 227 cm
2Area of 2 L-shaped sides
= 2 x 227
= 454 cm
2 Total surface area
= 12604 + 4232 + 454
= 17290 cm
2 Answer(s): (a) 375; (b) 17290 cm
2