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 Two pairs of identical semicircles have been cut out of a rectangular piece of paper of length 30 cm by 14 cm.  Find the area of the remaining piece of paper.  (Take = 3.14) [4 pts]

 Mar 18, 2023
 #1
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Draw a cicle inside a rectangle in such a way that , circumfrence touches both the lengths of rectangle. diameter = 14cm

Radius = 7cm. Area of circle (O)=154 cm^2 and area of rectangle (R)=4200cm^2 area left in rectangle = R-O

Answer = 4200-266

==> 3934cm^2

 Mar 18, 2023
 #2
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The area of the rectangular piece of paper is:

30 cm x 14 cm = 420 cm^2

 

Each semicircle has a radius of 7 cm (half of the width of the rectangular piece). The total area of the four semicircles is:

 

2 x (1/2) x pi x (7 cm)^2 + 2 x (1/2) x pi x (7 cm)^2
= 2 x (1/2) x pi x 49 cm^2 + 2 x (1/2) x pi x 49 cm^2
= 2 x pi x 24.5 cm^2 + 2 x pi x 24.5 cm^2
= 98 cm^2 x pi =307.88 cm^2 

 

Therefore, the area of the remaining piece of paper is:

 

420 cm^2 - 307.88 cm^2 x pi
= 112.12 cm^2 (rounded to two decimal place)

 Mar 18, 2023

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