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What is the radius of the circle whose area is equal to the sum of the areas of two circles whose radii are 20 cm and 21 cm?
- a)27m
- b)28m
- c)29m
- d)25m
- e)15m
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
What is the radius of the circle whose area is equal to the sum of the...
πR² = πr1² + πr2²
πR² = π(r1² + r2²)
R² = (400 + 441)
R = 29
πR² = π(r1² + r2²)
R² = (400 + 441)
R = 29
Most Upvoted Answer
What is the radius of the circle whose area is equal to the sum of the...
πR² = πr1² + πr2²
πR² = π(r1² + r2²)
R² = (400 + 441)
R = 29
πR² = π(r1² + r2²)
R² = (400 + 441)
R = 29
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Community Answer
What is the radius of the circle whose area is equal to the sum of the...
To find the radius of the circle whose area is equal to the sum of the areas of two circles with radii 20 cm and 21 cm, we can use the formula for the area of a circle, which is A = πr^2.
Let's calculate the areas of the two circles first:
Area of the first circle with radius 20 cm:
A1 = π(20)^2 = 400π
Area of the second circle with radius 21 cm:
A2 = π(21)^2 = 441π
The sum of the areas of these two circles is:
A_total = A1 + A2 = 400π + 441π = 841π
Now, let's find the radius of the circle with the same area as the sum of the two circles.
A_total = πr^2
Substituting the value of A_total, we have:
841π = πr^2
Dividing both sides of the equation by π, we get:
841 = r^2
Taking the square root of both sides, we have:
r = √841
r = 29
Therefore, the radius of the circle whose area is equal to the sum of the areas of the two circles with radii 20 cm and 21 cm is 29 cm.
Hence, option C (29m) is the correct answer.
Let's calculate the areas of the two circles first:
Area of the first circle with radius 20 cm:
A1 = π(20)^2 = 400π
Area of the second circle with radius 21 cm:
A2 = π(21)^2 = 441π
The sum of the areas of these two circles is:
A_total = A1 + A2 = 400π + 441π = 841π
Now, let's find the radius of the circle with the same area as the sum of the two circles.
A_total = πr^2
Substituting the value of A_total, we have:
841π = πr^2
Dividing both sides of the equation by π, we get:
841 = r^2
Taking the square root of both sides, we have:
r = √841
r = 29
Therefore, the radius of the circle whose area is equal to the sum of the areas of the two circles with radii 20 cm and 21 cm is 29 cm.
Hence, option C (29m) is the correct answer.
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