the external dimensions of a closed wooden box are 25 cm, 21 cm and 13 cm, if the thickness of the wood in the box is 1.5 cm, find: (1) volume of wood in the box (2) the cost of the box, if wood cost Rs 1.50 per cm3(3) no. of 5 cm cubes that could be placed into the box.

Dear Student,

Please find below the solution to the asked query:

Given : External dimensions of a closed wooden box are 25 cm, 21 cm and 13 cm, if the thickness of the wood in the box is 1.5 cm, So

Internal dimensions of closed wooden box = 25 - ( 1.5 $\times$ 2 ) = 22 cm , 21 - ( 1.5 $\times$ 2 ) = 18 cm and 13 - ( 1.5 $\times$ 2 ) = 10 cm

We know volume of cuboid  = Length $\times$ Breadth $\times$ Height

1 ) Volume of wood in the box  =  Volume of box with external dimension  - Volume of box with internal dimension

Volume of wood in the box  = 25 $\times$ 21 $\times$ 13  - 22 $\times$ 18 $\times$ 10

Volume of wood in the box  = 6825 - 3960

Volume of wood in the box  = 2865 cm³                                                      ( Ans ) 

2 ) Rate of the wood  Rs 1.50 per cm³ , So

Cost of the box  = 2865 $\times$ 1.50 = Rs . 4297.5                                             ( Ans )

3 ) We know volume of cube  = ( Side )³ , So

Volume of given cube  =  5³ =  125 cm³

And

Number of given cubes can be fit in wooden box  = $\frac{\mathrm{Volume} \mathrm{of} \mathrm{box} \mathrm{with} \mathrm{internal} \mathrm{dimension}}{\mathrm{Volume} \mathrm{of} \mathrm{cube}} = \frac{3960}{125} =\mathbf{31}\frac{\mathbf{15}}{\mathbf{125}}$

Therefore,

Number of given cubes can be fit in wooden box  = 31                                                   ( Ans )


Hope this information will clear your doubts about Surface Areas and Volumes .

If you have any more doubts just ask here on the forum and our experts will try to help you out as soon as possible.

Regards