Math, asked by justinbeiberfan, 14 days ago

Question for Only:- ❏ Moderators ❏ Brainly Stars ❏ Best users ✰ QUESTION ✰from a rectangular cardboard ABCD 2 circles and 1 semicircle of a largest side are cut. calculate the ratio between the area of the remaining cardboard and area of cardboard.​

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Answers

Answered by abhi569
2

Answer:

(1 - π/4) : 1    or   (π - 4):4    or  3 : 14

Step-by-step explanation:

let the radii of the circle(s) be 'r'.

Observing the figure, we get:

     Breadth of rect. = r + r = 2r

     Length of rect. = r + 2r + 2r = 5r

∴ Initially:  

        Area of rect. = l * b

                              = 5r * 2r

                              = 10r²

When the area of 2 circle and semi-cricle is cut:

⇒ Remaining area = Area of rectangle - [2ar. of circle + ar. of semi-circle + ar. of semi-circle]

⇒ Remaining area = 10r² - [2*πr² + 1/2 πr²]

                               = 10r² - (5/2)πr²

                               = 10r²[1 - π/4]

∴ Required ratio = 10r²(1 - π/4) : 10r²

                           = (1 - π/4) : 1

                  Or,    = (4 - π) : 4

Answered by jaswasri2006
1

Required Ratio = 10r²(1 - π/4) : 10r²

= (1-π/4) : 1

= (4 - π) : 4

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