The figure shows a rubber cuboid that measures 106 cm by 38 cm by 38 cm.
- Find the maximum number of 3-cm cubes that can be cut from the rubber cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 106 ÷ 3
= 35 r 1
Breath = Height
Number of cubes along the breadth or height
= 38 ÷ 3
= 12 r 2
Maximum number of 3 cm cubes
= 35 x 12 x 12
= 5040
(b)
Area of the 2 squares
= 2 x 38 x 38
= 2888 cm
2 Area of the top and bottom bases
= 2 x 106 x 38
= 8056 cm
2 Area of 1 L-shaped side
= 106 x 2 + (38 - 2) x 1
= 212 + 36
= 248 cm
2Area of 2 L-shaped sides
= 2 x 248
= 496 cm
2 Total surface area
= 8056 + 2888 + 496
= 11440 cm
2 Answer(s): (a) 5040; (b) 11440 cm
2