The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle having its area equal to the sum of the areas of the two circles.
Answers
Answered by
14
Answer:
The Radius of the circle is 10 cm
Step-by-step explanation:
SOLUTION :
Given :
Radius of first circle ,r1 = 8 cm
Radius of first circle ,r2 = 6 cm
Area of first circle , A1 = πr1²
A1 = π × 8²
A1 = 64π cm² …………(1)
Area of second circle, A2 = πr2²
A2 = π × 6²
A2 = 36π cm² ……..(2)
Area of circle, A = πr²
Area of circle = Sum of the areas of the two circles (Given)
A = A1 + A2
πr² = 64π + 36π
[From eq 1 & 2]
πr² = π(64 + 36)
r² = (64 + 36)
r² = 100
r = √100
r = 10 cm
Radius of the circle = 10 cm
Hence, the Radius of the circle is 10 cm
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Answered by
5
Answer :
10cm
Explanation:
Let R , r are radii of two circles.
R = 8cm , r = 6cm
Let radius of the new circle be
R1.
According to the problem given,
Area of the new circle = πR²+πr²
=> πR1² = π(R²+r²)
Divide both sides by π , we get
=>(R1)² = R²+r²
= 8²+6²
= 64+36
= 100
=> (R1)² = (10)²
R1 = 10 cm
Therefore,
Radius of the new circle = 10cm
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