The figure shows a rubber cuboid that measures 112 cm by 18 cm by 18 cm.
- Find the maximum number of 5-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
= 112 ÷ 5
= 22 r 2
Breath = Height
Number of cubes along the breadth or height
= 18 ÷ 5
= 3 r 3
Maximum number of 5 cm cubes
= 22 x 3 x 3
= 198
(b)
Area of the 2 squares
= 2 x 18 x 18
= 648 cm
2 Area of the top and bottom bases
= 2 x 112 x 18
= 4032 cm
2 Area of 1 L-shaped side
= 112 x 3 + (18 - 3) x 2
= 336 + 30
= 366 cm
2Area of 2 L-shaped sides
= 2 x 366
= 732 cm
2 Total surface area
= 4032 + 648 + 732
= 5412 cm
2 Answer(s): (a) 198; (b) 5412 cm
2