Question

The measure of an arc of a circle is 90° and its length is 11 cm. What is the diameter of the circle 2 (A) 21 cm (B) 7 cm (C) 14 cm (D) 28 cm

Answer 1

diameter is the 14cm here r= 7 diameter is= 2r

Answer 2

$\huge\underline\mathfrak{Answer}$

14 cm


$\huge\underline\mathfrak{Solution}$



$\textbf{Given}$



Measurement of arc of circle = 90°


Length of arc= 11cm



$\textbf{Formula,used}$


$s = r \alpha$

s= length of arc


r= radius of circle


$\alpha =angle \: by \: arc$




$\textbf{Step-by-step-Solutions}$



$s = r \alpha$
so,

$r = \frac{s}{ \alpha }$


$r = \frac{11}{ \alpha }$


alpha = 90°

$= 90 \times 1 = 90 \times \frac{\pi}{180}$


$= \frac{\pi}{2}$


so,


$r = \frac{11}{2 \times \pi}$


$r = \frac{22 \times 7}{22 }$

$r = 7cm$

$\textbf{Therefore}$



Diameter=2r

=2×7cm


=14cm