The figure shows a wooden cuboid that measures 139 cm by 16 cm by 16 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
= 139 ÷ 7
= 19 r 6
Breath = Height
Number of cubes along the breadth or height
= 16 ÷ 7
= 2 r 2
Maximum number of 7 cm cubes
= 19 x 2 x 2
= 76
(b)
Area of the 2 squares
= 2 x 16 x 16
= 512 cm
2 Area of the top and bottom bases
= 2 x 139 x 16
= 4448 cm
2 Area of 1 L-shaped side
= 139 x 2 + (16 - 2) x 6
= 278 + 84
= 362 cm
2Area of 2 L-shaped sides
= 2 x 362
= 724 cm
2 Total surface area
= 4448 + 512 + 724
= 5684 cm
2 Answer(s): (a) 76; (b) 5684 cm
2