The figure shows a wooden cuboid that measures 131 cm by 33 cm by 33 cm.
- Find the maximum number of 9-cm cubes that can be cut from the wooden cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 131 ÷ 9
= 14 r 5
Breath = Height
Number of cubes along the breadth or height
= 33 ÷ 9
= 3 r 6
Maximum number of 9 cm cubes
= 14 x 3 x 3
= 126
(b)
Area of the 2 squares
= 2 x 33 x 33
= 2178 cm
2 Area of the top and bottom bases
= 2 x 131 x 33
= 8646 cm
2 Area of 1 L-shaped side
= 131 x 6 + (33 - 6) x 5
= 786 + 135
= 921 cm
2Area of 2 L-shaped sides
= 2 x 921
= 1842 cm
2 Total surface area
= 8646 + 2178 + 1842
= 12666 cm
2 Answer(s): (a) 126; (b) 12666 cm
2