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 65 x 35
= 4550 cm2
2 painted areas breadthwise
= 2 x 45 x 35
= 3150 cm
2
Base painted area
= 65 x 45
= 2925 cm2
Painted areas
= 4550 + 3150 + 2925
= 10625 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 65 x 45 x 35
= 102375 cm
3 Number of 1-cm cubes in the box when full
= 102375 ÷ 1
= 102375
(c)
Number of cubes that touch the base of the box
= 65 x 45
= 2925
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 65 x (35 - 1)
= 2 x 65 x 34
= 4420
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (45 - 2) x (35 - 1)
= 2 x 43 x 34
= 2924
Number of cubes that touch the inside of the box
= 2925 + 4420 + 2924
= 10269
Answer(s): (a) 10625 cm
2; (b) 102375; (c) 10269