Question

Four equal circles, each of radius 5 cm, touch each other as shown in the following figure. Find the area included between them (Take π = 3.14).​

Answer 1

Answer:

The area of the shaded portion is 21.5 cm².

Step-by-step explanation:

Given :

Radius of a circle = 5 cm

Side of a square = 2 × Radius of a circle

= 2 × 5  

Side of a square = 10 cm  

Area of a square = Side²

Area of a square = 10² =100 cm²

Area of a square = 100 cm²

Area of the quadrant of one circle = 1/4πr²

Area of the quadrant of four circles = 4 × 1/4πr² = πr²  

= 3.14 × 5 × 5

=  3.14 × 25

= 78.5cm²

Area of the quadrant of four circles = 78.5cm²  

Area of the shaded portion, A = Area of the square – Area of the quadrant of four circles  

A = 100 – 78.5

A = 21.5 cm²

Area of the shaded portion = 21.5 cm²

Hence, the area of the shaded portion is 21.5 cm².

HOPE THIS ANSWER WILL HELP YOU….

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ABCDEF is a regular hexagon with centre O (in the following figure). If the area of triangle OAB is 9 cm², find the area of :  

(i)the hexagon and  

(ii)the circle in which the hexagon is inscribed.

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Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular card board of dimensions 14 cm × 7 cm. Find the area of the remaining card board. (Use $(\pi=\frac{22}{7})$).

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Answer 2

Answer:

Step-by-step explanation:

Area of the quadrant of four circles = 4 × 1/4πr² = πr²  

= 3.14 × 5 × 5

=  3.14 × 25

= 78.5cm²

Area of the quadrant of four circles = 78.5cm²  

Area of the shaded portion, A = Area of the square – Area of the quadrant of four circles  

A = 100 – 78.5

A = 21.5 cm²