Question

The diameter of a coin is 1 cm (in the following figure). If four such coins be placed on a table so that the rim of each touches that of the other two, find the area of the shaded region (Take π = 3.1416).​

Answer 1

Answer:

The area of the shaded portion is 42 cm².

Step-by-step explanation:

Given :  

Diameter of a coin (circle) = 1 cm

Radius of a coin (circle) ,r = Diameter of a coin (circle)/2

r = ½ = 0.5 cm

Radius of a coin (circle) ,r = 0.5 cm

Side of a square = 2 × Radius of a coin (circle)  

= 2 × 0.5  

= 1 cm

Side of a square = 1 cm

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

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

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

A = Side² - πr²

A = 1² - 3.1416 × (0.5)²

A = 1 - 3.1416 × 0.25

A = 1 - 0.7854

A = 0.2146 cm²

Area of the shaded portion = 0.2146 cm²

Hence, the area of the shaded portion is 42 cm².

HOPE THIS ANSWER WILL HELP YOU….

Here are more questions of the same chapter :

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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A child makes a poster on a chart paper drawing a square ABCD of side 14 cm. She draws four circles with centre A, B, C and D in which she suggests different ways to save energy. The circles are drawn in such a way that each circle touches externally two of the three remaining circles (in the following figure). Find the perimeter and area of the shaded region.

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Answer 2

hey mate

here is your answer.

Answer:

area of the shaded portion=area of the

square. - area of the 4 quadrants

From the figure given,

the side of the square=2*radii of the

circle

the side=diameter of the circle

the side=1 cm

we know that ,

1 circle=4 quadrants

thus,

area of the shaded portion=area of the

square. - area of the 1 circle

area of the shaded portion=1cm*1cm-

πr²

area of the shaded portion=1 cm²-

3.1416*0.5cm*0.5cm

area of the shaded portion=1 cm² - 3.1416*0.25 cm²

area of the shaded portion=1 cm² -0. 7854

area of the shaded portion=0.2146 cm²