The figure shows a wooden cuboid that measures 131 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
= 131 ÷ 4
= 32 r 3
Breath = Height
Number of cubes along the breadth or height
= 14 ÷ 4
= 3 r 2
Maximum number of 4 cm cubes
= 32 x 3 x 3
= 288
(b)
Area of the 2 squares
= 2 x 14 x 14
= 392 cm
2 Area of the top and bottom bases
= 2 x 131 x 14
= 3668 cm
2 Area of 1 L-shaped side
= 131 x 2 + (14 - 2) x 3
= 262 + 36
= 298 cm
2Area of 2 L-shaped sides
= 2 x 298
= 596 cm
2 Total surface area
= 3668 + 392 + 596
= 4656 cm
2 Answer(s): (a) 288; (b) 4656 cm
2