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If the radius of a circle is increased by 25%, its area increases by:
- A50 percent
- B25 percent
- C28.125 percent
- D56.25 percent
Answer not set
Discussion 1
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CCommunity
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%
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%