The figure shows a wooden cuboid that measures 102 m by 15 m by 15 m.
- Find the maximum number of 9-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
= 102 ÷ 9
= 11 r 3
Breath = Height
Number of cubes along the breadth or height
= 15 ÷ 9
= 1 r 6
Maximum number of 9 m cubes
= 11 x 1 x 1
= 11
(b)
Area of the 2 squares
= 2 x 15 x 15
= 450 m
2 Area of the top and bottom bases
= 2 x 102 x 15
= 3060 m
2 Area of 1 L-shaped side
= 102 x 6 + (15 - 6) x 3
= 612 + 27
= 639 m
2Area of 2 L-shaped sides
= 2 x 639
= 1278 m
2 Total surface area
= 3060 + 450 + 1278
= 4788 m
2 Answer(s): (a) 11; (b) 4788 m
2