2. 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
areas of the two circles.
Answers
Given :
- Radii of two circles :-
- Radius₁ = 8 cm
- Radius₂ = 6 cm
To find :
- The radius of the circle having area equal to the sum of the areas of the two circles.
Concept :
Formula to calculate area of circle :-
- Area of circle = πr²
where,
- Take π = 22/7
- r = radius of the circle
Solution :
As mentioned in the question, we will find the area of the two circles and add them.
→ πr²₁ + πr²₂ = πR²
→ Take π common from both the sides.
→ π(r²₁ + r²₂) = π(R²)
→ π will get cancelled.
→ r²₁ + r²₂ = R²
→ (8)² + (6)² = R²
→ 64 + 36 = R²
→ 100 = R²
→ Taking square root on both the sides.
→ √100 = R
→ ± 10 = R
→ As we know that radius cannot be negative. So, negative sign will get rejected.
→ ± 10 Reject - ve = R
→ 10 = R
Radius = 10 cm
Therefore,
- The radius of the circle having area equal to the sum of the areas of the two circles is 10 cm
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VERIFICATION :
To verify our answer substitue the value of the radii in πr²₁ + πr²₂ = πR².
Taking LHS,
→ πr²₁ + πr²₂
→ Take π common.
→ π(r²₁ + r²₂)
→ π((8)² + (6)²)
→ π(64 + 36)
→ π(100)
→ 100 π
LHS = 100 π
Taking RHS,
→ πR²
→ π (10)²
→ π(100)
→ 100 π
RHS = 100 π
LHS = RHS
HENCE, VERIFIED.