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1 mark

If the radius of a circle is increased by 25%, its area increases by:

  1. A
    50 percent
  2. B
    25 percent
  3. C
    28.125 percent
  4. D
    56.25 percent

Solution & Step-by-step Explanation

The area of a circle is proportional to the square of its radius (A∝r
2
).
When a quantity increases by x%, the effective percentage increase in its square is given by the successive percentage formula:

Percentage Increase=x+x+
100
x×x
​

Given x=25%:

Percentage Increase=25+25+
100
25×25
​

Percentage Increase=50+
100
625
​
=50+6.25=56.25%

Practice this question

Try it yourself before checking the explanation above.

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

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