The figure shows a metallic cuboid that measures 116 cm by 49 cm by 49 cm.
- Find the maximum number of 5-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 ÷ 5
= 23 r 1
Breath = Height
Number of cubes along the breadth or height
= 49 ÷ 5
= 9 r 4
Maximum number of 5 cm cubes
= 23 x 9 x 9
= 1863
(b)
Area of the 2 squares
= 2 x 49 x 49
= 4802 cm
2 Area of the top and bottom bases
= 2 x 116 x 49
= 11368 cm
2 Area of 1 L-shaped side
= 116 x 4 + (49 - 4) x 1
= 464 + 45
= 509 cm
2Area of 2 L-shaped sides
= 2 x 509
= 1018 cm
2 Total surface area
= 11368 + 4802 + 1018
= 17188 cm
2 Answer(s): (a) 1863; (b) 17188 cm
2