Question

3. The measure of the major arc of a circle is seven times
the measure of the corresponding minor arc. If the radius
of the circle is 14 cm then area of shaded region is :
​

Answer 1

$\mathfrak\red{given:}$

radius of circle=14 cm

ratio of major arc is to minor arc=7:1

$\mathfrak\red{to \:find:}$

area of shaded region.... i.e area of sector....

$\huge\math</strong><strong>c</strong><strong>a</strong><strong>l</strong><strong>\</strong><strong>b</strong><strong>l</strong><strong>u</strong><strong>e</strong><strong>{</strong><strong>SoLuTiOn</strong><strong>.</strong><strong>..!!!!}$

let,

measures of minor arc be 'x°'

so,

=>measures of major arc+measures of minor arc=360°

=>7x+x=360

=>x=360/8=45°

=>AREA OF SHADED REGION=1/2*r^2*θ

=>AREA OF SHADED REGION=1/2*14^2*45....(θ=x°)

=>AREA OF SHADED REGION=98*45=4410 cm^2

$<marquee>area of shaded region=4410 cm^2...</marquee>$

hope it helps!!☺