The figure shows a rubber cuboid that measures 117 cm by 27 cm by 27 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
= 117 ÷ 7
= 16 r 5
Breath = Height
Number of cubes along the breadth or height
= 27 ÷ 7
= 3 r 6
Maximum number of 7 cm cubes
= 16 x 3 x 3
= 144
(b)
Area of the 2 squares
= 2 x 27 x 27
= 1458 cm
2 Area of the top and bottom bases
= 2 x 117 x 27
= 6318 cm
2 Area of 1 L-shaped side
= 117 x 6 + (27 - 6) x 5
= 702 + 105
= 807 cm
2Area of 2 L-shaped sides
= 2 x 807
= 1614 cm
2 Total surface area
= 6318 + 1458 + 1614
= 9390 cm
2 Answer(s): (a) 144; (b) 9390 cm
2