PSLE An open rectangular box is shown.
- The inside of the box including the base is painted. Find the painted area.
- When the box is packed full with 1-cm cubes, how many cubes are there?
- How many cubes touch inside the box as a result?
(a)
2 painted areas lengthwise
= 2 x 50 x 20
= 2000 cm2
2 painted areas breadthwise
= 2 x 25 x 20
= 1000 cm
2
Base painted area
= 50 x 25
= 1250 cm2
Painted areas
= 2000 + 1000 + 1250
= 4250 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 50 x 25 x 20
= 25000 cm
3 Number of 1-cm cubes in the box when full
= 25000 ÷ 1
= 25000
(c)
Number of cubes that touch the base of the box
= 50 x 25
= 1250
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 50 x (20 - 1)
= 2 x 50 x 19
= 1900
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (25 - 2) x (20 - 1)
= 2 x 23 x 19
= 874
Number of cubes that touch the inside of the box
= 1250 + 1900 + 874
= 4024
Answer(s): (a) 4250 cm
2; (b) 25000; (c) 4024