The figure shows a rubber cuboid that measures 110 cm by 48 cm by 48 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
= 110 ÷ 7
= 15 r 5
Breath = Height
Number of cubes along the breadth or height
= 48 ÷ 7
= 6 r 6
Maximum number of 7 cm cubes
= 15 x 6 x 6
= 540
(b)
Area of the 2 squares
= 2 x 48 x 48
= 4608 cm
2 Area of the top and bottom bases
= 2 x 110 x 48
= 10560 cm
2 Area of 1 L-shaped side
= 110 x 6 + (48 - 6) x 5
= 660 + 210
= 870 cm
2Area of 2 L-shaped sides
= 2 x 870
= 1740 cm
2 Total surface area
= 10560 + 4608 + 1740
= 16908 cm
2 Answer(s): (a) 540; (b) 16908 cm
2