The figure shows a rubber cuboid that measures 101 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
= 101 ÷ 5
= 20 r 1
Breath = Height
Number of cubes along the breadth or height
= 18 ÷ 5
= 3 r 3
Maximum number of 5 cm cubes
= 20 x 3 x 3
= 180
(b)
Area of the 2 squares
= 2 x 18 x 18
= 648 cm
2 Area of the top and bottom bases
= 2 x 101 x 18
= 3636 cm
2 Area of 1 L-shaped side
= 101 x 3 + (18 - 3) x 1
= 303 + 15
= 318 cm
2Area of 2 L-shaped sides
= 2 x 318
= 636 cm
2 Total surface area
= 3636 + 648 + 636
= 4920 cm
2 Answer(s): (a) 180; (b) 4920 cm
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