Question

The ratio of radius of a circle and the side of a square is 2 : 11. find the ratio of their areas:

Answer 1

Concept:

A circle's area is the area that it takes up in a two-dimensional plane. It can be simply calculated using the formula A = πr², (Pi r-squared), where r is the circle's radius. The square unit, such as m², cm², etc., is the unit of area.

Area of Circle = πr² or πd²/4, square units

where π = 22/7 or 3.14

The quantity of square units required to completely fill a square is known as the area of a square. The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area. Measurements are made in square units, with square metres serving as the reference unit (m²).

Area of square =a²

where, a=side length

Given:

The ratio of radius of a circle and the side of a square is 2 : 11.

Find:

Find the ratio of area of circle to ratio of square.

Solution:

Ratio of radius of circle/radius of square=2/11

r/a=2/11-----------------i

So,

Area of circle / Area of square =πr²/a²

                                                   =π(2/11)²

                                                    =π4/121

                                                   =(22 x 4 )/(7x121  )

                                                    =8:77

Therefore, the ratio of area of circle to area of square =8:77

#SPJ2

Answer 2

Given the ratio of the radius of a circle and the side of a square is 2 : 11.

Let the radius of the circle is $2x$ and the side of $11x$ .

We know the area of the circle is $\pi r^2 \ unit^2$ , where r = radius of the circle and the area of the square is $a^2 \ unit^2$ , where a = side of the square.

Therefore, we get the ratio

$\pi (2x)^2 : (11x)^2\\= \frac{22}{7} \times 2x \times 2x : 11x \times 11x\\=\frac{2}{7} \times 4 : 11\\=\frac{8}{7} : 11\\=8 : 11 \times 7\\=8 : 77$

Therefore the required ratio of the area of the circle and the area of the square is 8 : 77.

To learn more about the area of a circle from the given link

https://brainly.in/question/1829122

#SPJ2