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 55 x 35
= 3850 cm2
2 painted areas breadthwise
= 2 x 38 x 35
= 2660 cm
2
Base painted area
= 55 x 38
= 2090 cm2
Painted areas
= 3850 + 2660 + 2090
= 8600 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 55 x 38 x 35
= 73150 cm
3 Number of 1-cm cubes in the box when full
= 73150 ÷ 1
= 73150
(c)
Number of cubes that touch the base of the box
= 55 x 38
= 2090
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 55 x (35 - 1)
= 2 x 55 x 34
= 3740
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (38 - 2) x (35 - 1)
= 2 x 36 x 34
= 2448
Number of cubes that touch the inside of the box
= 2090 + 3740 + 2448
= 8278
Answer(s): (a) 8600 cm
2; (b) 73150; (c) 8278