The figure shows a metallic cuboid that measures 133 cm by 42 cm by 42 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
= 133 ÷ 4
= 33 r 1
Breath = Height
Number of cubes along the breadth or height
= 42 ÷ 4
= 10 r 2
Maximum number of 4 cm cubes
= 33 x 10 x 10
= 3300
(b)
Area of the 2 squares
= 2 x 42 x 42
= 3528 cm
2 Area of the top and bottom bases
= 2 x 133 x 42
= 11172 cm
2 Area of 1 L-shaped side
= 133 x 2 + (42 - 2) x 1
= 266 + 40
= 306 cm
2Area of 2 L-shaped sides
= 2 x 306
= 612 cm
2 Total surface area
= 11172 + 3528 + 612
= 15312 cm
2 Answer(s): (a) 3300; (b) 15312 cm
2