The figure shows a wooden cuboid that measures 111 cm by 34 cm by 34 cm.
- Find the maximum number of 8-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
= 111 ÷ 8
= 13 r 7
Breath = Height
Number of cubes along the breadth or height
= 34 ÷ 8
= 4 r 2
Maximum number of 8 cm cubes
= 13 x 4 x 4
= 208
(b)
Area of the 2 squares
= 2 x 34 x 34
= 2312 cm
2 Area of the top and bottom bases
= 2 x 111 x 34
= 7548 cm
2 Area of 1 L-shaped side
= 111 x 2 + (34 - 2) x 7
= 222 + 224
= 446 cm
2Area of 2 L-shaped sides
= 2 x 446
= 892 cm
2 Total surface area
= 7548 + 2312 + 892
= 10752 cm
2 Answer(s): (a) 208; (b) 10752 cm
2