Question

Question for Only:- ❏ Moderators ❏ Brainly Stars ❏ Best users ✰ QUESTIONfrom 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

see your ans from attached pic...

Answer 2

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

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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 = $\sf 10r² - \bigg( 2πr² + \frac{πr²}{2} \bigg)$

• Area of remaining cardboard = $\sf 10r² - \bigg(\frac{4πr² + πr²}{2} \bigg)$

• Area of remaining cardboard = $\sf 10r² - \frac{5πr²}{2}$

• Area of remaining cardboard = $\sf \bigg( \frac{20 {r}^{2} - 5 \frac{22}{7} {r}^{2} }{2} \bigg)$

• Area of remaining cardboard = $\sf \cancel2 \bigg( \frac{10 {r}^{2} - 5 \times \frac{11}{7} {r}^{2}}{ \cancel2} \bigg)$

• Area of remaining cardboard = $\sf \bigg(10 {r}^{2} - 5 \times \frac{11}{7} {r}^{2} \bigg)$

• Area of remaining cardboard = $\sf \bigg( \frac{70 {r}^{2} - 55 {r}^{2}}{7} \bigg)$

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

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

• Ratio = $\sf \frac{the \: \: area \: \: of \: \: the \: \: remaining \: \: cardboard}{area \: \: of \: \: cardboard}$

• Ratio = $\sf \frac{\bigg( \frac{15 {r}^{2} }{7} \bigg)}{10 \: \: r²}$

• Ratio = $\sf \frac{15 \cancel{ {r}^{2}} }{7 \times 10 \cancel{ {r}^{2} }}$

• Ratio = $\sf \frac{ \cancel5 \times 3}{7 \times \cancel5 \times 2}$

• Ratio = $\sf \frac{3}{14}$

• Ratio = $\large \sf {\underline{ 3 : 14 }}$

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I hope it helps you ❤️✔️

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