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Grade -10 (SEE) Math

Solution of Area related to Circles

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

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CTEVT > Diploma/PCL > PCL In Medical Lab Technology Revised 2019

Solution:
Given,
The radius of the 1st circle = 8 cm 
∴ Area of the 1st circle = 𝜋 (8)2 = 64𝜋 
The radius of the 2nd circle = 6 cm 
∴ Area of the 2nd circle = 𝜋 (6)2  = 36𝜋 

So,
The sum of the Area of two circles = 64𝜋 + 36𝜋 = 100𝜋 
Now, assume that the radius of the 3rd circle = R
∴ The Area of the 3rd circle = 𝜋R2
It is given that the area of the 3rd circle = Area of 1st circle + Area of 2nd circle
Or, 𝜋R2 = 100𝜋 cm2
        R2 = 100 cm2
    So, R = 10 cm

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