Question

The length of a cubical carton is 2 m. How many cubical chalk-stick boxes with length 25 cm can be packed in it.

Answer 1

Hint: Given length of a cubical carton and a cubical chalk-stick box as 2 m and 25 cm respectively. So first find the volume of the carton and volume of one chalk-stick box separately. To find the no. of chalk-stick boxes that can be packed in the carton, divide the volume of the carton by the volume of one chalk-stick box.
Formula used:
Volume of a cube with side a is $ {a^3} $

Complete step by step solution:
We are given that length of a cubical carton and a cubical chalk-stick box as 2 m and 25 cm respectively. We have to find the no. of chalk-stick boxes that can be packed in the carton.

Volume of the carton with length 2 m is $ {2^3} = 8\;{m^3} $
1 metre is equal to 100 centimetres.
1 cubic metre is equal to $ {10^6} $ centimetres.
This means $ 8\;{m^3} = 8 \times {10^6}\;c{m^3} $
Volume of the chalk-stick box with length 25 cm is $ {25^3} = 15625\;c{m^3} $
Total no. of chalk-stick boxes that can be packed in the carton is n.
 $ \Rightarrow n = \dfrac{{Volum{e_{carton}}}}{{Volum{e_{chalkstick\_box}}}} $
 $ \Rightarrow n = \dfrac{{8 \times {{10}^6}}}{{15625}} = 512 $
Therefore, 512 cubical chalk-stick boxes can be packed in the cubicle cartoon.
So, the correct answer is “512”.

Note: A cube and a cuboid both have 6 faces, 12 edges and 8 vertices. Length, breadth and height are different in a cuboid, whereas they are equal in a cube. All the cubes are cuboids but all the cuboids are not cubes. While dividing the same quantities, their units must also be the same. That is why we have converted the volume of carton from cubic metres to cubic centimetres. We can also convert the volume of the chalk-stick box into cubic metres.