The figure shows a rubber cuboid that measures 150 cm by 16 cm by 16 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
= 150 ÷ 7
= 21 r 3
Breath = Height
Number of cubes along the breadth or height
= 16 ÷ 7
= 2 r 2
Maximum number of 7 cm cubes
= 21 x 2 x 2
= 84
(b)
Area of the 2 squares
= 2 x 16 x 16
= 512 cm
2 Area of the top and bottom bases
= 2 x 150 x 16
= 4800 cm
2 Area of 1 L-shaped side
= 150 x 2 + (16 - 2) x 3
= 300 + 42
= 342 cm
2Area of 2 L-shaped sides
= 2 x 342
= 684 cm
2 Total surface area
= 4800 + 512 + 684
= 5996 cm
2 Answer(s): (a) 84; (b) 5996 cm
2