The figure shows a rubber cuboid that measures 109 cm by 20 cm by 20 cm.
- Find the maximum number of 7-cm cubes that can be cut from the rubber cuboid.
- Find the total surface area of the L-shaped block after cutting.
(a)
Number of cubes along the length
= 109 ÷ 7
= 15 r 4
Breath = Height
Number of cubes along the breadth or height
= 20 ÷ 7
= 2 r 6
Maximum number of 7 cm cubes
= 15 x 2 x 2
= 60
(b)
Area of the 2 squares
= 2 x 20 x 20
= 800 cm
2 Area of the top and bottom bases
= 2 x 109 x 20
= 4360 cm
2 Area of 1 L-shaped side
= 109 x 6 + (20 - 6) x 4
= 654 + 56
= 710 cm
2Area of 2 L-shaped sides
= 2 x 710
= 1420 cm
2 Total surface area
= 4360 + 800 + 1420
= 6580 cm
2 Answer(s): (a) 60; (b) 6580 cm
2