The figure shows a rubber cuboid that measures 100 cm by 43 cm by 43 cm.
- Find the maximum number of 6-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
= 100 ÷ 6
= 16 r 4
Breath = Height
Number of cubes along the breadth or height
= 43 ÷ 6
= 7 r 1
Maximum number of 6 cm cubes
= 16 x 7 x 7
= 784
(b)
Area of the 2 squares
= 2 x 43 x 43
= 3698 cm
2 Area of the top and bottom bases
= 2 x 100 x 43
= 8600 cm
2 Area of 1 L-shaped side
= 100 x 1 + (43 - 1) x 4
= 100 + 168
= 268 cm
2Area of 2 L-shaped sides
= 2 x 268
= 536 cm
2 Total surface area
= 8600 + 3698 + 536
= 12834 cm
2 Answer(s): (a) 784; (b) 12834 cm
2