The figure shows a wooden cuboid that measures 137 cm by 34 cm by 34 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
= 137 ÷ 9
= 15 r 2
Breath = Height
Number of cubes along the breadth or height
= 34 ÷ 9
= 3 r 7
Maximum number of 9 cm cubes
= 15 x 3 x 3
= 135
(b)
Area of the 2 squares
= 2 x 34 x 34
= 2312 cm
2 Area of the top and bottom bases
= 2 x 137 x 34
= 9316 cm
2 Area of 1 L-shaped side
= 137 x 7 + (34 - 7) x 2
= 959 + 54
= 1013 cm
2Area of 2 L-shaped sides
= 2 x 1013
= 2026 cm
2 Total surface area
= 9316 + 2312 + 2026
= 13654 cm
2 Answer(s): (a) 135; (b) 13654 cm
2