Question

Find the volume of wood used in making a closed box 22 cm by 18 cm by 14 cm, using a 1 cm thick wood. Also, find the cost of wood required to make the box at the rate of Rs. 5 per cm³ How many cubes of side 2 cm can be placed in the box?

Answer 1

Thickness of the closed box = 1cm
External Dimensions are:
l = 22cm
b = 18cm
h = 14cm
Internal dimensions = External dimensions - 2(thickness)
Internal dimensions are:
l = 20cm
b = 16cm
h = 12cm
Volume of wood used in making the box
= Volume of External cuboid - Volume of Internal cuboid
= (22 x 18 x 14) - (20 x 16 x 12)
= 5544 - 3840
= 1704cm³
∴ The volume of the wood used in making the box is 1704cm³.    ...(Ans 1)
The cost of the wood required to make the box at the rate of Rs.5per cm³
= 5 x 1704
= Rs. 8520   ...(Ans 2)
Side of the cube = 2cm
∴ Volume of the cube = 8cm³
Volume of the box from inside = Volume of internal cuboid
= 20 x 16 x 12
= 3840cm³
∴ The no. of cubes that can fit inside the box

= `"Volume of internal cuboid"/"Volume of each small cube"`

= `(3840)/(8)`
= 480 cubes.   ...(Ans 3)