The figure shows a rubber cuboid that measures 137 cm by 15 cm by 15 cm.
- Find the maximum number of 8-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
= 137 ÷ 8
= 17 r 1
Breath = Height
Number of cubes along the breadth or height
= 15 ÷ 8
= 1 r 7
Maximum number of 8 cm cubes
= 17 x 1 x 1
= 17
(b)
Area of the 2 squares
= 2 x 15 x 15
= 450 cm
2 Area of the top and bottom bases
= 2 x 137 x 15
= 4110 cm
2 Area of 1 L-shaped side
= 137 x 7 + (15 - 7) x 1
= 959 + 8
= 967 cm
2Area of 2 L-shaped sides
= 2 x 967
= 1934 cm
2 Total surface area
= 4110 + 450 + 1934
= 6494 cm
2 Answer(s): (a) 17; (b) 6494 cm
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