The figure shows a plastic cuboid that measures 143 cm by 43 cm by 43 cm.
- Find the maximum number of 5-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
= 143 ÷ 5
= 28 r 3
Breath = Height
Number of cubes along the breadth or height
= 43 ÷ 5
= 8 r 3
Maximum number of 5 cm cubes
= 28 x 8 x 8
= 1792
(b)
Area of the 2 squares
= 2 x 43 x 43
= 3698 cm
2 Area of the top and bottom bases
= 2 x 143 x 43
= 12298 cm
2 Area of 1 L-shaped side
= 143 x 3 + (43 - 3) x 3
= 429 + 120
= 549 cm
2Area of 2 L-shaped sides
= 2 x 549
= 1098 cm
2 Total surface area
= 12298 + 3698 + 1098
= 17094 cm
2 Answer(s): (a) 1792; (b) 17094 cm
2