The figure shows a rubber cuboid that measures 104 cm by 33 cm by 33 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
= 104 ÷ 9
= 11 r 5
Breath = Height
Number of cubes along the breadth or height
= 33 ÷ 9
= 3 r 6
Maximum number of 9 cm cubes
= 11 x 3 x 3
= 99
(b)
Area of the 2 squares
= 2 x 33 x 33
= 2178 cm
2 Area of the top and bottom bases
= 2 x 104 x 33
= 6864 cm
2 Area of 1 L-shaped side
= 104 x 6 + (33 - 6) x 5
= 624 + 135
= 759 cm
2Area of 2 L-shaped sides
= 2 x 759
= 1518 cm
2 Total surface area
= 6864 + 2178 + 1518
= 10560 cm
2 Answer(s): (a) 99; (b) 10560 cm
2