The figure shows a rubber cuboid that measures 114 cm by 44 cm by 44 cm.
- Find the maximum number of 7-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
= 114 ÷ 7
= 16 r 2
Breath = Height
Number of cubes along the breadth or height
= 44 ÷ 7
= 6 r 2
Maximum number of 7 cm cubes
= 16 x 6 x 6
= 576
(b)
Area of the 2 squares
= 2 x 44 x 44
= 3872 cm
2 Area of the top and bottom bases
= 2 x 114 x 44
= 10032 cm
2 Area of 1 L-shaped side
= 114 x 2 + (44 - 2) x 2
= 228 + 84
= 312 cm
2Area of 2 L-shaped sides
= 2 x 312
= 624 cm
2 Total surface area
= 10032 + 3872 + 624
= 14528 cm
2 Answer(s): (a) 576; (b) 14528 cm
2