The figure shows a wooden cuboid that measures 109 cm by 17 cm by 17 cm.
- Find the maximum number of 4-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
= 109 ÷ 4
= 27 r 1
Breath = Height
Number of cubes along the breadth or height
= 17 ÷ 4
= 4 r 1
Maximum number of 4 cm cubes
= 27 x 4 x 4
= 432
(b)
Area of the 2 squares
= 2 x 17 x 17
= 578 cm
2 Area of the top and bottom bases
= 2 x 109 x 17
= 3706 cm
2 Area of 1 L-shaped side
= 109 x 1 + (17 - 1) x 1
= 109 + 16
= 125 cm
2Area of 2 L-shaped sides
= 2 x 125
= 250 cm
2 Total surface area
= 3706 + 578 + 250
= 4534 cm
2 Answer(s): (a) 432; (b) 4534 cm
2