The figure shows a plastic cuboid that measures 109 cm by 10 cm by 10 cm.
- Find the maximum number of 3-cm cubes that can be cut from the plastic cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 109 ÷ 3
= 36 r 1
Breath = Height
Number of cubes along the breadth or height
= 10 ÷ 3
= 3 r 1
Maximum number of 3 cm cubes
= 36 x 3 x 3
= 324
(b)
Area of the 2 squares
= 2 x 10 x 10
= 200 cm
2 Area of the top and bottom bases
= 2 x 109 x 10
= 2180 cm
2 Area of 1 L-shaped side
= 109 x 1 + (10 - 1) x 1
= 109 + 9
= 118 cm
2Area of 2 L-shaped sides
= 2 x 118
= 236 cm
2 Total surface area
= 2180 + 200 + 236
= 2616 cm
2 Answer(s): (a) 324; (b) 2616 cm
2