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If the radius of a circle is increased by 25%, its area increases by:
- a)50 percent
- b)25 percent
- c)28.125 percent
- d)56.25 percent
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
If the radius of a circle is increased by 25%, its area increases by:a...
Let the radius of the circle be x cm.
So, area = πx2 cm2.
The radius of a circle is increased by 25%.
So, the increased radius = x × (125/100) = 5x/4 cm
Now, area = π × (5x/4)2 cm2 = 25πx2/16 cm2
So, increase in area = (25πx2/16) – πx2 = 9πx2/16 cm2
∴ The required percentage change = [{(9πx2/16)/πx2} × 100% = 56.25%
Most Upvoted Answer
If the radius of a circle is increased by 25%, its area increases by:a...
Explanation:
To solve this problem, let's consider the formula for the area of a circle:
A = πr^2
Where:
A = Area of the circle
π = Pi, approximately 3.14159
r = Radius of the circle
Step 1: Calculate the original area of the circle
Let the original radius be 'r'. Therefore, the original area is:
A1 = πr^2
Step 2: Calculate the new radius after increasing it by 25%
If the radius is increased by 25%, the new radius will be:
New radius = r + (25/100) * r = r + 0.25r = 1.25r
Step 3: Calculate the new area of the circle
Using the new radius, the new area is given by:
A2 = π(1.25r)^2 = π(1.5625r^2) = 1.5625πr^2
Step 4: Calculate the percentage increase in area
To find the percentage increase in the area, we can use the formula:
Percentage Increase = (New Area - Original Area) / Original Area * 100
Substituting the values:
Percentage Increase = (1.5625πr^2 - πr^2) / πr^2 * 100 = 0.5625 * 100 = 56.25%
Therefore, the area of the circle increases by 56.25% when the radius is increased by 25%.
The correct answer is option 'D' (56.25 percent).
To solve this problem, let's consider the formula for the area of a circle:
A = πr^2
Where:
A = Area of the circle
π = Pi, approximately 3.14159
r = Radius of the circle
Step 1: Calculate the original area of the circle
Let the original radius be 'r'. Therefore, the original area is:
A1 = πr^2
Step 2: Calculate the new radius after increasing it by 25%
If the radius is increased by 25%, the new radius will be:
New radius = r + (25/100) * r = r + 0.25r = 1.25r
Step 3: Calculate the new area of the circle
Using the new radius, the new area is given by:
A2 = π(1.25r)^2 = π(1.5625r^2) = 1.5625πr^2
Step 4: Calculate the percentage increase in area
To find the percentage increase in the area, we can use the formula:
Percentage Increase = (New Area - Original Area) / Original Area * 100
Substituting the values:
Percentage Increase = (1.5625πr^2 - πr^2) / πr^2 * 100 = 0.5625 * 100 = 56.25%
Therefore, the area of the circle increases by 56.25% when the radius is increased by 25%.
The correct answer is option 'D' (56.25 percent).
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If the radius of a circle is increased by 25%, its area increases by:a)50 percentb)25 percentc)28.125 percentd)56.25 percentCorrect answer is option 'D'. Can you explain this answer?
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