The figure shows a rubber cuboid that measures 131 cm by 22 cm by 22 cm.
- Find the maximum number of 9-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
= 131 ÷ 9
= 14 r 5
Breath = Height
Number of cubes along the breadth or height
= 22 ÷ 9
= 2 r 4
Maximum number of 9 cm cubes
= 14 x 2 x 2
= 56
(b)
Area of the 2 squares
= 2 x 22 x 22
= 968 cm
2 Area of the top and bottom bases
= 2 x 131 x 22
= 5764 cm
2 Area of 1 L-shaped side
= 131 x 4 + (22 - 4) x 5
= 524 + 90
= 614 cm
2Area of 2 L-shaped sides
= 2 x 614
= 1228 cm
2 Total surface area
= 5764 + 968 + 1228
= 7960 cm
2 Answer(s): (a) 56; (b) 7960 cm
2