Question

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.​

Answer 1

Answer:

Answer :-

For area of remaining cardboard,

Area of remaining cardboard = Area of 2 circles + Area of 1 semicircle

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Area of Circle = πr²

For Area of 2 Circle = 2πr²

Area of 1 semicircle = \sf \frac{1}{2} πr²21πr²

Area of 1 semicircle = \sf \frac{πr²}{2}2πr²

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Now,

Area of rectangular cupboard = L × b

L = r + 2r + 2r = 5r

b = 2r

Area of rectangular cupboard = L × b

Area of rectangular cupboard = ( 5r × 2r )

Area of rectangular cupboard = 10 r²

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Now,

Area of remaining cardboard = Area of rectangular cupboard - ( Area of 2 circles + Area of 1 semicircle )

Area of remaining cardboard = \begin{gathered} \sf 10r² - \bigg( 2πr² + \frac{πr²}{2} \bigg) \\ \end{gathered}10r²−(2πr²+2πr²)

Area of remaining cardboard = \begin{gathered} \sf 10r² - \bigg(\frac{4πr² + πr²}{2} \bigg) \\ \end{gathered}10r²−(24πr²+πr²)

Area of remaining cardboard = \begin{gathered} \sf 10r² - \frac{5πr²}{2} \\ \end{gathered}10r²−25πr²

Area of remaining cardboard = \begin{gathered} \sf \bigg( \frac{20 {r}^{2} - 5 \frac{22}{7} {r}^{2} }{2} \bigg) \\ \end{gathered}(220r2−5722r2)

Area of remaining cardboard = \begin{gathered} \sf \cancel2 \bigg( \frac{10 {r}^{2} - 5 \times \frac{11}{7} {r}^{2}}{ \cancel2} \bigg) \\ \end{gathered}2(210r2−5×711r2)

Area of remaining cardboard = \begin{gathered} \sf \bigg(10 {r}^{2} - 5 \times \frac{11}{7} {r}^{2} \bigg) \\ \end{gathered}(10r2−5×711r2)

Area of remaining cardboard = \begin{gathered} \sf \bigg( \frac{70 {r}^{2} - 55 {r}^{2}}{7} \bigg) \\ \end{gathered}(770r2−55r2)

Area of remaining cardboard = \sf \bigg( \frac{15 {r}^{2} }{7} \bigg)(715r2)

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Now, finally Ratio between the area of the remaining cardboard and area of cardboard.

Ratio = \begin{gathered} \sf \frac{the \: \: area \: \: of \: \: the \: \: remaining \: \: cardboard}{area \: \: of \: \: cardboard} \\ \end{gathered}areaofcardboardtheareaoftheremainingcardboard

Ratio = \begin{gathered} \sf \frac{\bigg( \frac{15 {r}^{2} }{7} \bigg)}{10 \: \: r²}\\ \end{gathered}10r²(715r2)

Ratio = \begin{gathered} \sf \frac{15 \cancel{ {r}^{2}} }{7 \times 10 \cancel{ {r}^{2} }} \\ \end{gathered}7×10r215r2

Ratio = \begin{gathered} \sf \frac{ \cancel5 \times 3}{7 \times \cancel5 \times 2} \\ \end{gathered}7×5×25×3

Ratio = \begin{gathered} \sf \frac{3}{14} \\ \end{gathered}143

Ratio = \begin{gathered} \large \sf {\underline{ 3 : 14 }} \\ \end{gathered}3:14

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I hope it helps you ❤️✔️

I'm sorry I took too long time to calculate.