The figure shows a wooden cuboid that measures 117 cm by 26 cm by 26 cm.
- Find the maximum number of 7-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
= 117 ÷ 7
= 16 r 5
Breath = Height
Number of cubes along the breadth or height
= 26 ÷ 7
= 3 r 5
Maximum number of 7 cm cubes
= 16 x 3 x 3
= 144
(b)
Area of the 2 squares
= 2 x 26 x 26
= 1352 cm
2 Area of the top and bottom bases
= 2 x 117 x 26
= 6084 cm
2 Area of 1 L-shaped side
= 117 x 5 + (26 - 5) x 5
= 585 + 105
= 690 cm
2Area of 2 L-shaped sides
= 2 x 690
= 1380 cm
2 Total surface area
= 6084 + 1352 + 1380
= 8816 cm
2 Answer(s): (a) 144; (b) 8816 cm
2