Question

The area of a rectangle and the area of a circle are equal. If the dimensions of the
rectangle are 14cm x 11 cm, then what is the radius of the circle?
Your answer​

Answer 1

Answer:

Radius of the circle is 7cm.

✳SOLUTION✳

Given in the question that,

Area of a rectangle = Area of a circle

It is also said in the question that the dimensions of the rectangle are 14cm x 11 cm.

We have to find the radius of the circle.

$\red \bigstar \boxed { \sf Area \:of \:Rectangle = Length(l)\: *\: Breadth (b)}$

Length(l) = 14cm.

Breadth(b) = 11cm.

$\implies$

Area of the rectangle = 14 × 11

$\implies$

Area of the rectangle = 154cm².

Now,

Area of the rectangle = Area of the circle

$\implies$

154 = πr²

✳Putting , π = 22/7

$\sf 154 = \dfrac{22}{7} * r^2$

$\implies$

154 × 7 = 22 × r²

$\implies$

1078 = 22r²

$\implies$

$\sf r^2 = \dfrac{1078}{22}$

$\implies$

r² = 49

$\implies$

$\sf r = \sqrt{49}$

$\implies$

r = 7cm.

The Circle is :-

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\qbezier(2.3,0)(2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,2.121)(0,2.3)\qbezier(-2.3,0)(-2.121,-2.121)(0,-2.3)\qbezier(2.3,0)(2.121,-2.121)(-0,-2.3)\put(0,0){\line(1,0){2.3}}\put(0.5,0.3){\bf\large 7\ cm}\end{picture}$

Answer 2

Answer:

12.4cm

Step-by-step explanation:

Area of rectangle = L x B

                            =  14 x 11

                           =  154 cm^2

Area of Circle and Area of rectangle are equal,

Area of Circle = π x r^2                           (π = 22/7)

          154 cm^2 = π x r^2

          154 x 7/22 = r^2                                   (dividing 154 and 22/7)

           22 x 7  =  r^2

            154   =   r^2

           √154 = r

           12.4 = r