The figure shows a wooden cuboid that measures 135 cm by 14 cm by 14 cm.
- Find the maximum number of 4-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
= 135 ÷ 4
= 33 r 3
Breath = Height
Number of cubes along the breadth or height
= 14 ÷ 4
= 3 r 2
Maximum number of 4 cm cubes
= 33 x 3 x 3
= 297
(b)
Area of the 2 squares
= 2 x 14 x 14
= 392 cm
2 Area of the top and bottom bases
= 2 x 135 x 14
= 3780 cm
2 Area of 1 L-shaped side
= 135 x 2 + (14 - 2) x 3
= 270 + 36
= 306 cm
2Area of 2 L-shaped sides
= 2 x 306
= 612 cm
2 Total surface area
= 3780 + 392 + 612
= 4784 cm
2 Answer(s): (a) 297; (b) 4784 cm
2