The figure shows a wooden cuboid that measures 114 cm by 10 cm by 10 cm.
- Find the maximum number of 7-cm cubes that can be cut from the wooden cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 114 ÷ 7
= 16 r 2
Breath = Height
Number of cubes along the breadth or height
= 10 ÷ 7
= 1 r 3
Maximum number of 7 cm cubes
= 16 x 1 x 1
= 16
(b)
Area of the 2 squares
= 2 x 10 x 10
= 200 cm
2 Area of the top and bottom bases
= 2 x 114 x 10
= 2280 cm
2 Area of 1 L-shaped side
= 114 x 3 + (10 - 3) x 2
= 342 + 14
= 356 cm
2Area of 2 L-shaped sides
= 2 x 356
= 712 cm
2 Total surface area
= 2280 + 200 + 712
= 3192 cm
2 Answer(s): (a) 16; (b) 3192 cm
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