Question

the outer dimension of a jewellery box made of wood are 20cm × 16cm × 8cm the thickness of wood is 1cm. find the total cost of wood required to make the box, if 1cm cube of wood costs rs2.50

Answer 1

Answer:

2620 Rs

Step-by-step explanation:

The givens are:

• Outer length = 20 cm
• Outer width = 16 cm
• Outer height = 8 cm

Therefore, outer volume = Length*Width*Height = 20*16*8 = 2560 $cm^3.$

Since the thickness of the wooden box is 1 cm,

Inner length = 20-2(1) = 18 cm

Inner width = 16-2(1) = 14 cm

Inner height = 8-2(1) = 6 cm

Therefore, the inner volume = 18*14*6 = 1512 $cm^3.$

Therefore, the volume of the wood used = Outer volume - Inner Volume = 2560-1512 = 1048 $cm^3.$

Since the cost of 1 $cm^3$ = 2.5 Rs, therefore, the total cost = 2.5*1048 = 2620 Rs

Answer 2

Solution:

Since jewellery box is in the shape of a cuboid,and how much amount of wood is required make can be calculated by finding external and internal Volume of the box.

External Volume of Box
$= l \: \times b \times h \\ \\ = 20 \times 16 \times 8 \\ \\ = 2560 \: {cm}^{3}$
Internal Volume:
Since Wood's Thickness is 1 cm

So all three dimensions are to be subtracted by 2,since thickness is along both the sides of length,breadth and height

l = 18 cm

b = 14 cm

h = 6 cm

$= 18 \times 14 \times 6 \\ \\ = 1512 \: {cm}^{3}$
Wood used to make that box =External Volume - Internal Volume

$= 2560 - 1512 \\ \\ = 1048 {cm}^{3}$

1cm cube of wood costs rs2.50

So 1048 cm-cube wood costs

$= 1048 \times 2.50 \\ \\ = 2620 \: Rs$