Question

Q.2- A plastic box 1.5 m long. 1.25 m wide and 65 cm deep is to be made. It is opened at the top.
Ignoring the thickness of the plastic sheet, determine the area of the sheet required for making the
box ) The cost of sheet for it, f a sheet measuring 2 1m costs Rs. 20
​

Answer 1

★ Answer ★

↠The area of the sheet required for making the box is 5.45 m²

↠The cost of sheet is Rs. 109 , if a sheet measuring 1 m² costs Rs. 20.

Step by step Explanation

★ Given :-

• Length = 1.5 m
• Breadth = 1.25 m
• Height = 65 cm

Converting it in " cm "

• Length of the box in cm = 150 cm
• Width of the box in cm = 125 m

★ Have to find :-

1. The area of the sheet required for making the box.
2. The cost of sheet for it, if a sheet measuring 1 m² costs Rs. 20.

Diagram:-

$\setlength{\unitlength}{6}\begin{picture}(10,6) \put(0,1){\line(0,1){10}}\put(0,1){\line(1,0){10}}\put(10,1){\line(0,1){10}}\put(0,11){\line(1,0){10}}\put(0,11){\line(1,1){5}}\put(10,11){\line(1,1){5}}\put(10,1){\line(1,1){5}}\put(0,1){\line(1,1){5}}\put(5,6){\line(1,0){10}}\put(5,6){\line(0,1){10}}\put(5,16){\line(1,0){10}}\put(15,6){\line(0,1){10}}\put(2, - 0.5){ \bf 1.5 m }\put(13,3){ \bf 1.25 m }\put( - 5, 5){ \bf 0.65 m }\end{picture}$

★ Solution:-

As we know , the box is in cuboidal shape.

Now, As according to the Question

Box is opened at the top.

The area of the sheet required for making the box.

Using the forumula of T.S.A

↬ Area = TSA - Area of Top

↬ 2(lb + bh + hl) - lb

↬ 2lb + 2bh +2hl - lb

↬ lb + 2bh + 2hl

↬Area =( 150 × 125 ) + [ 2 × ( 125 × 65 ) ] + [2 × (65 × 150)]

↬ 18,750 + (2 × 8,125) + (2 × 9,750)

↬ 18,750 + 16,250 + 19,500

↬ 54,500 cm²

Firstly converting it into m²

↬ Area of sheet in m² = 5.45 m²

Now, let's find out the cost of sheet for it,

1m² costs given as Rs 20

Then,

Total Cost of Sheet = Area of sheet × Cost

↬ 5.45 m² × Rs. 20

↬ Rs. 109

➤ Cost of Sheet is Rs. 109

____________________________

Answer 2

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━

${ \bold { \underline{\large\purple{Given : - }}}} \:$

❍ A plastic box 1.5 m long , 1.25 m wide ㅤand 65 cm deep. It is opened from top.

${ \bold { \underline{\large\pink{To \: Find : - }}}} \:$

❍ Area of the box.

❍ Cost of sheet for making it.

${ \bold { \underline{\large\green{Diagram : - }}}} \:$

$\setlength{\unitlength}{0.74 cm}\begin{picture}\thicklines\put(5.6,5.4){\bf A}\put(11.1,5.4){\bf B}\put(11.2,9){\bf C}\put(5.3,8.6){\bf D}\put(3.3,10.2){\bf E}\put(3.3,7){\bf F}\put(9.25,10.35){\bf H}\put(9.35,7.35){\bf G}\put(3.5,6.1){\sf 1.25\:cm}\put(7.7,6.3){\sf 1.5\:cm}\put(11.3,7.45){\sf 65\:cm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

${ \bold { \underline{\large\red{Solution : - }}}} \:$

Firstly changing all values from m to cm :-

1 m = 100cm

•°• we will multiply them by 100.

• Length :-

$\longmapsto$ $\sf{1.5\:\times\:100}$

$\longmapsto$ $\boxed{\sf{150\:cm}}\:\red\bigstar$

• Width :-

$\longmapsto$ $\sf{1.25\:\times\:100}$

$\longmapsto$ $\boxed{\sf{125\:cm}}\:\green\bigstar$

It's height is already in cm! So, no need to change it!

• Area of the box :-

$\longmapsto\:\sf{(Total \:surface \:area \:of box)\: - \:(Area\: of \:top\: face)}$

$\longmapsto$ $\sf{2(lb\:+\:bh\:+\:hl)\:-\:(lb)}$

$\longmapsto\:\sf{2[(150\:\times\:125)\:+\:(125\:\times\:65)\:+\:(65\:\times\:150)]\:-\:(150\:\times\:125)}$

$\longmapsto$ $\sf{2(18750\:+\:8125\:+\:9750)\:-\:(18750)}$

$\longmapsto$ $\sf{2(36625)\:-\:(18750)}$

$\longmapsto$ $\sf{(2\:\times\:36625)\:-\:(18750)}$

$\longmapsto$ $\sf{73250\:-\:18750}$

$\longmapsto$ $\boxed{\sf{54500}}\:\pink\bigstar$

•°• Area of box = 54500 cm².

Area of box in m² :-

$\longmapsto$ $\sf{\dfrac{54500}{10000}}$

$\longmapsto$ $\boxed{\sf{5.45\:m^2}}\:\orange\bigstar$

Now,

• Cost of sheet for making box , if it costs Rs. 20 for 1 m² :-

➱ Area of box × 20

➱ 5.45 × 20

➱ 109

•°• Cost of sheet for making box = Rs. 109.

Note :-

Kindly see the diagram from site. (brainly.in)

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━