The figure shows a metallic cuboid that measures 118 cm by 30 cm by 30 cm.
- Find the maximum number of 4-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
= 118 ÷ 4
= 29 r 2
Breath = Height
Number of cubes along the breadth or height
= 30 ÷ 4
= 7 r 2
Maximum number of 4 cm cubes
= 29 x 7 x 7
= 1421
(b)
Area of the 2 squares
= 2 x 30 x 30
= 1800 cm
2 Area of the top and bottom bases
= 2 x 118 x 30
= 7080 cm
2 Area of 1 L-shaped side
= 118 x 2 + (30 - 2) x 2
= 236 + 56
= 292 cm
2Area of 2 L-shaped sides
= 2 x 292
= 584 cm
2 Total surface area
= 7080 + 1800 + 584
= 9464 cm
2 Answer(s): (a) 1421; (b) 9464 cm
2