The figure shows a rubber cuboid that measures 135 cm by 33 cm by 33 cm.
- Find the maximum number of 6-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
= 135 ÷ 6
= 22 r 3
Breath = Height
Number of cubes along the breadth or height
= 33 ÷ 6
= 5 r 3
Maximum number of 6 cm cubes
= 22 x 5 x 5
= 550
(b)
Area of the 2 squares
= 2 x 33 x 33
= 2178 cm
2 Area of the top and bottom bases
= 2 x 135 x 33
= 8910 cm
2 Area of 1 L-shaped side
= 135 x 3 + (33 - 3) x 3
= 405 + 90
= 495 cm
2Area of 2 L-shaped sides
= 2 x 495
= 990 cm
2 Total surface area
= 8910 + 2178 + 990
= 12078 cm
2 Answer(s): (a) 550; (b) 12078 cm
2