The figure shows a metallic cuboid that measures 109 cm by 37 cm by 37 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
= 109 ÷ 8
= 13 r 5
Breath = Height
Number of cubes along the breadth or height
= 37 ÷ 8
= 4 r 5
Maximum number of 8 cm cubes
= 13 x 4 x 4
= 208
(b)
Area of the 2 squares
= 2 x 37 x 37
= 2738 cm
2 Area of the top and bottom bases
= 2 x 109 x 37
= 8066 cm
2 Area of 1 L-shaped side
= 109 x 5 + (37 - 5) x 5
= 545 + 160
= 705 cm
2Area of 2 L-shaped sides
= 2 x 705
= 1410 cm
2 Total surface area
= 8066 + 2738 + 1410
= 12214 cm
2 Answer(s): (a) 208; (b) 12214 cm
2