The figure shows a metallic cuboid that measures 116 cm by 34 cm by 34 cm.
- Find the maximum number of 8-cm cubes that can be cut from the metallic cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 116 ÷ 8
= 14 r 4
Breath = Height
Number of cubes along the breadth or height
= 34 ÷ 8
= 4 r 2
Maximum number of 8 cm cubes
= 14 x 4 x 4
= 224
(b)
Area of the 2 squares
= 2 x 34 x 34
= 2312 cm
2 Area of the top and bottom bases
= 2 x 116 x 34
= 7888 cm
2 Area of 1 L-shaped side
= 116 x 2 + (34 - 2) x 4
= 232 + 128
= 360 cm
2Area of 2 L-shaped sides
= 2 x 360
= 720 cm
2 Total surface area
= 7888 + 2312 + 720
= 10920 cm
2 Answer(s): (a) 224; (b) 10920 cm
2