Question

four equal circles are described at the four corners of a square so that each circle touches two of the others. find the area of the space enclosed between the circumferences of the circles each side of the square measuring 14 cm

Answer 1

Dear User!

Question:

Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces.

Method of Solution:

Given: Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces.

Now,

Area of Square (ABCD) = Side × Side

Area of Square (ABCD) = 14×14 cm²


Area of Square (ABCD) =196m²

Now, There are four Quadrant in a Square which are given in attachment!

Area of 4 Quadrant = (4×1/4×πr²)

Area of 4 Quadrant =22×7 cm²

Area of 4 Quadrant = 154cm²

Therefore, Area of portion= of Square (ABCD) - Area of 4 Square



Area of portion= 196-154 cm²

Area of portion = 42 cm²


Hence, Required Area of portion enclosed between these pieces are 42cm².

Answer 2

here is your answer OK ☺☺☺☺☺


here is your answer OK ☺☺☺☺☺

Area of each of the 4 sectors is equal to each other and is a sector of 90° in a circle of 7 cm radius.

area of each sector =
$\frac{90}{360} \times ({7}^{2} )$

= 1/4 x 22/7 x 7 x 7

= 77/2 cm'2

Area of square ABCD = (Side)2 = (14)2 = 196 cm2

Area of shaded portion = Area of square ABCD − 4 × Area of each sector

196-4 x 77/2 = 196 - 154

42 answer OK ☺☺☺☺

Therefore, the area of shaded portion is 42 cm2.



note : it's copies from my profile OK ☺☺☺