The figure shows a wooden cuboid that measures 111 cm by 36 cm by 36 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
= 111 ÷ 7
= 15 r 6
Breath = Height
Number of cubes along the breadth or height
= 36 ÷ 7
= 5 r 1
Maximum number of 7 cm cubes
= 15 x 5 x 5
= 375
(b)
Area of the 2 squares
= 2 x 36 x 36
= 2592 cm
2 Area of the top and bottom bases
= 2 x 111 x 36
= 7992 cm
2 Area of 1 L-shaped side
= 111 x 1 + (36 - 1) x 6
= 111 + 210
= 321 cm
2Area of 2 L-shaped sides
= 2 x 321
= 642 cm
2 Total surface area
= 7992 + 2592 + 642
= 11226 cm
2 Answer(s): (a) 375; (b) 11226 cm
2