The figure shows a rubber cuboid that measures 139 cm by 44 cm by 44 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
= 139 ÷ 9
= 15 r 4
Breath = Height
Number of cubes along the breadth or height
= 44 ÷ 9
= 4 r 8
Maximum number of 9 cm cubes
= 15 x 4 x 4
= 240
(b)
Area of the 2 squares
= 2 x 44 x 44
= 3872 cm
2 Area of the top and bottom bases
= 2 x 139 x 44
= 12232 cm
2 Area of 1 L-shaped side
= 139 x 8 + (44 - 8) x 4
= 1112 + 144
= 1256 cm
2Area of 2 L-shaped sides
= 2 x 1256
= 2512 cm
2 Total surface area
= 12232 + 3872 + 2512
= 18616 cm
2 Answer(s): (a) 240; (b) 18616 cm
2