The figure shows a rubber cuboid that measures 102 cm by 32 cm by 32 cm.
- Find the maximum number of 9-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
= 102 ÷ 9
= 11 r 3
Breath = Height
Number of cubes along the breadth or height
= 32 ÷ 9
= 3 r 5
Maximum number of 9 cm cubes
= 11 x 3 x 3
= 99
(b)
Area of the 2 squares
= 2 x 32 x 32
= 2048 cm
2 Area of the top and bottom bases
= 2 x 102 x 32
= 6528 cm
2 Area of 1 L-shaped side
= 102 x 5 + (32 - 5) x 3
= 510 + 81
= 591 cm
2Area of 2 L-shaped sides
= 2 x 591
= 1182 cm
2 Total surface area
= 6528 + 2048 + 1182
= 9758 cm
2 Answer(s): (a) 99; (b) 9758 cm
2