The figure shows a wooden cuboid that measures 136 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
= 136 ÷ 3
= 45 r 1
Breath = Height
Number of cubes along the breadth or height
= 13 ÷ 3
= 4 r 1
Maximum number of 3 cm cubes
= 45 x 4 x 4
= 720
(b)
Area of the 2 squares
= 2 x 13 x 13
= 338 cm
2 Area of the top and bottom bases
= 2 x 136 x 13
= 3536 cm
2 Area of 1 L-shaped side
= 136 x 1 + (13 - 1) x 1
= 136 + 12
= 148 cm
2Area of 2 L-shaped sides
= 2 x 148
= 296 cm
2 Total surface area
= 3536 + 338 + 296
= 4170 cm
2 Answer(s): (a) 720; (b) 4170 cm
2