The figure shows a wooden cuboid that measures 117 m by 33 m by 33 m.
- Find the maximum number of 7-m 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
= 117 ÷ 7
= 16 r 5
Breath = Height
Number of cubes along the breadth or height
= 33 ÷ 7
= 4 r 5
Maximum number of 7 m cubes
= 16 x 4 x 4
= 256
(b)
Area of the 2 squares
= 2 x 33 x 33
= 2178 m
2 Area of the top and bottom bases
= 2 x 117 x 33
= 7722 m
2 Area of 1 L-shaped side
= 117 x 5 + (33 - 5) x 5
= 585 + 140
= 725 m
2Area of 2 L-shaped sides
= 2 x 725
= 1450 m
2 Total surface area
= 7722 + 2178 + 1450
= 11350 m
2 Answer(s): (a) 256; (b) 11350 m
2