The figure shows a plastic cuboid that measures 111 cm by 18 cm by 18 cm.
- Find the maximum number of 8-cm cubes that can be cut from the plastic cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 111 ÷ 8
= 13 r 7
Breath = Height
Number of cubes along the breadth or height
= 18 ÷ 8
= 2 r 2
Maximum number of 8 cm cubes
= 13 x 2 x 2
= 52
(b)
Area of the 2 squares
= 2 x 18 x 18
= 648 cm
2 Area of the top and bottom bases
= 2 x 111 x 18
= 3996 cm
2 Area of 1 L-shaped side
= 111 x 2 + (18 - 2) x 7
= 222 + 112
= 334 cm
2Area of 2 L-shaped sides
= 2 x 334
= 668 cm
2 Total surface area
= 3996 + 648 + 668
= 5312 cm
2 Answer(s): (a) 52; (b) 5312 cm
2