The figure shows a wooden cuboid that measures 110 cm by 43 cm by 43 cm.
- Find the maximum number of 3-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
= 110 ÷ 3
= 36 r 2
Breath = Height
Number of cubes along the breadth or height
= 43 ÷ 3
= 14 r 1
Maximum number of 3 cm cubes
= 36 x 14 x 14
= 7056
(b)
Area of the 2 squares
= 2 x 43 x 43
= 3698 cm
2 Area of the top and bottom bases
= 2 x 110 x 43
= 9460 cm
2 Area of 1 L-shaped side
= 110 x 1 + (43 - 1) x 2
= 110 + 84
= 194 cm
2Area of 2 L-shaped sides
= 2 x 194
= 388 cm
2 Total surface area
= 9460 + 3698 + 388
= 13546 cm
2 Answer(s): (a) 7056; (b) 13546 cm
2