The figure shows a wooden cuboid that measures 138 cm by 16 cm by 16 cm.
- Find the maximum number of 5-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
= 138 ÷ 5
= 27 r 3
Breath = Height
Number of cubes along the breadth or height
= 16 ÷ 5
= 3 r 1
Maximum number of 5 cm cubes
= 27 x 3 x 3
= 243
(b)
Area of the 2 squares
= 2 x 16 x 16
= 512 cm
2 Area of the top and bottom bases
= 2 x 138 x 16
= 4416 cm
2 Area of 1 L-shaped side
= 138 x 1 + (16 - 1) x 3
= 138 + 45
= 183 cm
2Area of 2 L-shaped sides
= 2 x 183
= 366 cm
2 Total surface area
= 4416 + 512 + 366
= 5294 cm
2 Answer(s): (a) 243; (b) 5294 cm
2