The figure shows a wooden cuboid that measures 131 cm by 13 cm by 13 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
= 131 ÷ 3
= 43 r 2
Breath = Height
Number of cubes along the breadth or height
= 13 ÷ 3
= 4 r 1
Maximum number of 3 cm cubes
= 43 x 4 x 4
= 688
(b)
Area of the 2 squares
= 2 x 13 x 13
= 338 cm
2 Area of the top and bottom bases
= 2 x 131 x 13
= 3406 cm
2 Area of 1 L-shaped side
= 131 x 1 + (13 - 1) x 2
= 131 + 24
= 155 cm
2Area of 2 L-shaped sides
= 2 x 155
= 310 cm
2 Total surface area
= 3406 + 338 + 310
= 4054 cm
2 Answer(s): (a) 688; (b) 4054 cm
2