The figure shows a metallic cuboid that measures 103 cm by 36 cm by 36 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
= 103 ÷ 5
= 20 r 3
Breath = Height
Number of cubes along the breadth or height
= 36 ÷ 5
= 7 r 1
Maximum number of 5 cm cubes
= 20 x 7 x 7
= 980
(b)
Area of the 2 squares
= 2 x 36 x 36
= 2592 cm
2 Area of the top and bottom bases
= 2 x 103 x 36
= 7416 cm
2 Area of 1 L-shaped side
= 103 x 1 + (36 - 1) x 3
= 103 + 105
= 208 cm
2Area of 2 L-shaped sides
= 2 x 208
= 416 cm
2 Total surface area
= 7416 + 2592 + 416
= 10424 cm
2 Answer(s): (a) 980; (b) 10424 cm
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