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 44 x 65
= 5720 cm2
2 painted areas breadthwise
= 2 x 35 x 65
= 4550 cm
2
Base painted area
= 44 x 35
= 1540 cm2
Painted areas
= 5720 + 4550 + 1540
= 11810 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 44 x 35 x 65
= 100100 cm
3 Number of 1-cm cubes in the box when full
= 100100 ÷ 1
= 100100
(c)
Number of cubes that touch the base of the box
= 44 x 35
= 1540
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x (65 - 1) x 44
= 2 x 64 x 44
= 5632
Number of cubes that touch the 2 faces breathwise excluding the base
= 2 x (35 - 2) x (65 - 1)
= 2 x 33 x 64
= 4224
Number of cubes that touch the inside of the box
= 1540 + 5632 + 4224
= 11396
Answer(s): (a) 11810 cm
2; (b) 100100; (c) 11396