Question

The external dimensions of a closed wooden box are 27 cm, 19 cm, and 11 cm. If the thickness of the wood in the box is 1.5 cm; find:

1. The volume of the wood in the box;
2. The cost of the box, if wood costs Rs. 1.20 per cm³;
3. A number of 4 cm cubes that could be placed into the box.

Answer 1

External volume of the box 
= 27 × 19  × 11 cm³ = 5643 cm³

Since external dimensions are 27 cm, 19 cm, and 11 cm, the thickness of the wood is 1.5 cm.

Internal dimensions of the box 
= ( 27 - 2  × 1.5 ) cm, ( 19 - 2  × 1.5 )cm, ( 11 - 2  × 1.5 ) cm
= 24 cm, 16 cm, 8 cm

Hence, the internal volume of box = ( 24  × 16  × 8 ) cm³ = 3072 cm³

1. The volume of wood in the box = 5643 cm³ - 3072 cm³ = 2571 cm³
2. Cost of wood = Rs. 1.20  × 2571
   = Rs. 3085.2
3. Volume. of 4 cm cube = 4³ = 64 cm³
4. Number of 4 cm cubes that could be placed into the box
   = `3072/64`
   =  48 cubes.