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 35 x 15
= 1050 cm2
2 painted areas breadthwise
= 2 x 20 x 15
= 600 cm
2
Base painted area
= 35 x 20
= 700 cm2
Painted areas
= 1050 + 600 + 700
= 2350 cm
2 (b)
Volume of 1 cube
= 1 x 1 x 1
= 1 cm
3 Volume of the box
= 35 x 20 x 15
= 10500 cm
3 Number of 1-cm cubes in the box when full
= 10500 ÷ 1
= 10500
(c)
Number of cubes that touch the base of the box
= 35 x 20
= 700
Number of cubes that touch the 2 faces lengthwise excluding the base
= 2 x 35 x (15 - 1)
= 2 x 35 x 14
= 980
Number of cubes that touch the 2 faces breadthwise excluding the base
= 2 x (20 - 2) x (15 - 1)
= 2 x 18 x 14
= 504
Number of cubes that touch the inside of the box
= 700 + 980 + 504
= 2184
Answer(s): (a) 2350 cm
2; (b) 10500; (c) 2184