The figure shows a plastic cuboid that measures 143 cm by 33 cm by 33 cm.
- Find the maximum number of 7-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 ÷ 7
= 20 r 3
Breath = Height
Number of cubes along the breadth or height
= 33 ÷ 7
= 4 r 5
Maximum number of 7 cm cubes
= 20 x 4 x 4
= 320
(b)
Area of the 2 squares
= 2 x 33 x 33
= 2178 cm
2 Area of the top and bottom bases
= 2 x 143 x 33
= 9438 cm
2 Area of 1 L-shaped side
= 143 x 5 + (33 - 5) x 3
= 715 + 84
= 799 cm
2Area of 2 L-shaped sides
= 2 x 799
= 1598 cm
2 Total surface area
= 9438 + 2178 + 1598
= 13214 cm
2 Answer(s): (a) 320; (b) 13214 cm
2