The figure shows a rubber cuboid that measures 127 cm by 17 cm by 17 cm.
- Find the maximum number of 3-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
= 127 ÷ 3
= 42 r 1
Breath = Height
Number of cubes along the breadth or height
= 17 ÷ 3
= 5 r 2
Maximum number of 3 cm cubes
= 42 x 5 x 5
= 1050
(b)
Area of the 2 squares
= 2 x 17 x 17
= 578 cm
2 Area of the top and bottom bases
= 2 x 127 x 17
= 4318 cm
2 Area of 1 L-shaped side
= 127 x 2 + (17 - 2) x 1
= 254 + 15
= 269 cm
2Area of 2 L-shaped sides
= 2 x 269
= 538 cm
2 Total surface area
= 4318 + 578 + 538
= 5434 cm
2 Answer(s): (a) 1050; (b) 5434 cm
2