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]
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
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)
