The figure shows a metallic cuboid that measures 138 cm by 24 cm by 24 cm.
- Find the maximum number of 7-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
= 138 ÷ 7
= 19 r 5
Breath = Height
Number of cubes along the breadth or height
= 24 ÷ 7
= 3 r 3
Maximum number of 7 cm cubes
= 19 x 3 x 3
= 171
(b)
Area of the 2 squares
= 2 x 24 x 24
= 1152 cm
2 Area of the top and bottom bases
= 2 x 138 x 24
= 6624 cm
2 Area of 1 L-shaped side
= 138 x 3 + (24 - 3) x 5
= 414 + 105
= 519 cm
2Area of 2 L-shaped sides
= 2 x 519
= 1038 cm
2 Total surface area
= 6624 + 1152 + 1038
= 8814 cm
2 Answer(s): (a) 171; (b) 8814 cm
2