The figure shows a metallic cuboid that measures 122 cm by 25 cm by 25 cm.
- Find the maximum number of 9-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
= 122 ÷ 9
= 13 r 5
Breath = Height
Number of cubes along the breadth or height
= 25 ÷ 9
= 2 r 7
Maximum number of 9 cm cubes
= 13 x 2 x 2
= 52
(b)
Area of the 2 squares
= 2 x 25 x 25
= 1250 cm
2 Area of the top and bottom bases
= 2 x 122 x 25
= 6100 cm
2 Area of 1 L-shaped side
= 122 x 7 + (25 - 7) x 5
= 854 + 90
= 944 cm
2Area of 2 L-shaped sides
= 2 x 944
= 1888 cm
2 Total surface area
= 6100 + 1250 + 1888
= 9238 cm
2 Answer(s): (a) 52; (b) 9238 cm
2