The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the area of the twi circles

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter8: Areas Of Polygons And Circles
Section8.4: Cicumference And Area Of A Cicle
Problem 33E: The radii of two concentric circles differ in length by exactly 1 in. If their areas differ by...
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The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having area equal to the sum of the area of the twi circles

Expert Solution
Step 1

Given, Radius of first circle = 8 cm 

Radius of second circle = 6 cm .

 

Step 2

Required Area of Circle = Area of circle having radius 8 cm + Area of circle having radius 6 cm

{ Area of circle is given as = π * ( radius)2}

=> πr2 = π(8)2+ π(6)2 

=> πr2= 64π + 36 π

=> r2 = 100

=>  r = √100 = 10 cm 

 

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