The figure shows a wooden cuboid that measures 127 cm by 14 cm by 14 cm.
- Find the maximum number of 5-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
= 127 ÷ 5
= 25 r 2
Breath = Height
Number of cubes along the breadth or height
= 14 ÷ 5
= 2 r 4
Maximum number of 5 cm cubes
= 25 x 2 x 2
= 100
(b)
Area of the 2 squares
= 2 x 14 x 14
= 392 cm
2 Area of the top and bottom bases
= 2 x 127 x 14
= 3556 cm
2 Area of 1 L-shaped side
= 127 x 4 + (14 - 4) x 2
= 508 + 20
= 528 cm
2Area of 2 L-shaped sides
= 2 x 528
= 1056 cm
2 Total surface area
= 3556 + 392 + 1056
= 5004 cm
2 Answer(s): (a) 100; (b) 5004 cm
2