The figure shows a plastic cuboid that measures 111 cm by 35 cm by 35 cm.
- Find the maximum number of 6-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 ÷ 6
= 18 r 3
Breath = Height
Number of cubes along the breadth or height
= 35 ÷ 6
= 5 r 5
Maximum number of 6 cm cubes
= 18 x 5 x 5
= 450
(b)
Area of the 2 squares
= 2 x 35 x 35
= 2450 cm
2 Area of the top and bottom bases
= 2 x 111 x 35
= 7770 cm
2 Area of 1 L-shaped side
= 111 x 5 + (35 - 5) x 3
= 555 + 90
= 645 cm
2Area of 2 L-shaped sides
= 2 x 645
= 1290 cm
2 Total surface area
= 7770 + 2450 + 1290
= 11510 cm
2 Answer(s): (a) 450; (b) 11510 cm
2