Question

The length, breadth and height of a closed wooden box are 20 cm, 12 cm and 8 cm. The thickness of the wood used to make the box is 10 mm. Find:
(1) the volume of the wood.
(ii) the cost of the wood required to make the box, if 1 cm of wood costs rupees 8.50​

Answer 1

Part 1: The volume of the wood is $840 \ cm}^{3}$

Part 2: The cost of the wood required to make the box is $Rs.\ 7140$

Explanation:

It is given that $l=20$ , $b=12$ and $h=8$

Part 1: The volume of the wooden box can be determined by subtracting the outer volume of the box and the inner volume of the box.

It is given that the thickness of the wood is 10mm = 1 cm

The inner dimensions of the wooden box are:

$l=20-(2\times1)=18\ cm$

$b=12-(2\times 1)=10 \ cm$

$h=8-(2\times1)=6 \ cm$

The outer volume of the wooden box is

$V= l\times b \times h$

$V=20\times12\times8$

$V=1920 \ cm^3$

The inner volume of the wooden box is

$V= l\times b \times h$

$V=18\times 10 \times 6$

$V=1080 \ cm^3$

Volume of the wood = Volume of the outer box - Volume of the inner box

Volume of the wooden box = $1920-1080$

                                              $=840 \ cm^3$

Thus, the volume of the wood is $840 \ cm}^{3}$

Part 2: It is given that 1 cm of wood costs Rs. 8.50

The cost of wood required to make the box is given by,

Cost of wood = $840 \times 8 .50$

                       $=7140$

Thus, the cost of the wood required to make the box is $Rs.\ 7140$

Learn more:

(1) The length , breadth and height of a closed wooden box are 20cm , 12cm & 8cm. The thickness of the wood used to make the box is 10mm. Find:

(i) the volume of the wood

(ii) the cost of the wood required to make the box , if 1cm³ of the wood costs 8.50Rs.

brainly.in/question/15423719

(2) The outer dimensions of a closed wooden box are 10 cm by 8 cm by 7cm. Thickness of the wood is 1 cm. Find the total cost of the wood required to make box if 1 cm3 of wood cost 2 rupees.

brainly.in/question/1117152

Answer 2

Step-by-step explanation:

The inner dimensions of the wooden box are:

l=20-(2\times1)=18\

cml=20−(2×1)=18 cm

b=12-(2\times 1)=10 \ cmb=12−(2×1)=10 cm

h=8-(2\times1)=6 \ cmh=8−(2×1)=6 cm

The outer volume of the wooden box is

V= l\times b \times hV=l×b×h

V=20\times12\times8V=20×12×8

V=1920 \ cm^3V=1920 cm3

The inner volume of the wooden box is

V= l\times b \times hV=l×b×h

V=18\times 10 \times 6V=18×10×6

V=1080 \ cm^3V=1080 cm3

Volume of the wood = Volume of the outer box - Volume of the inner box

Volume of the wooden box = 1920-10801920−1080

                                              =840 \ cm^3=840 cm3

Thus, the volume of the wood is 840 \ cm}^{3}

Part 2: It is given that 1 cm of wood costs Rs. 8.50

The cost of wood required to make the box is given by,

Cost of wood = 840 \times 8 .50840×8.50

                       =7140=7140