The figure shows a wooden cuboid that measures 109 cm by 21 cm by 21 cm.
- Find the maximum number of 8-cm cubes that can be cut from the wooden 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
= 21 ÷ 8
= 2 r 5
Maximum number of 8 cm cubes
= 13 x 2 x 2
= 52
(b)
Area of the 2 squares
= 2 x 21 x 21
= 882 cm
2 Area of the top and bottom bases
= 2 x 109 x 21
= 4578 cm
2 Area of 1 L-shaped side
= 109 x 5 + (21 - 5) x 5
= 545 + 80
= 625 cm
2Area of 2 L-shaped sides
= 2 x 625
= 1250 cm
2 Total surface area
= 4578 + 882 + 1250
= 6710 cm
2 Answer(s): (a) 52; (b) 6710 cm
2