The radius of a circle is increased by 2cm from 5 cm to 7 cm . What is the percentage change in area of the circle ?

Options

A. `96%`
B. `35%`
C. `70%`
D. `74%`

Answer

To find the percentage change in the area of a circle when the radius is increased from 5 cm to 7 cm, we can follow these steps:

### Step 1: Calculate the area of the circle with the initial radius (R1 = 5 cm).
The formula for the area of a circle is given by:
\[ \text{Area} = \pi R^2 \]

So, for R1:
\[ \text{Area}_1 = \pi (5)^2 = \pi \times 25 = 25\pi \, \text{cm}^2 \]

### Step 2: Calculate the area of the circle with the new radius (R2 = 7 cm).
Using the same formula:
\[ \text{Area}_2 = \pi (7)^2 = \pi \times 49 = 49\pi \, \text{cm}^2 \]

### Step 3: Calculate the change in area.
The change in area is given by:
\[ \text{Change in Area} = \text{Area}_2 - \text{Area}_1 \]
\[ \text{Change in Area} = 49\pi - 25\pi = (49 - 25)\pi = 24\pi \, \text{cm}^2 \]

### Step 4: Calculate the percentage change in area.
The percentage change can be calculated using the formula:
\[ \text{Percentage Change} = \left( \frac{\text{Change in Area}}{\text{Area}_1} \right) \times 100 \]
Substituting the values we found:
\[ \text{Percentage Change} = \left( \frac{24\pi}{25\pi} \right) \times 100 \]

The \(\pi\) cancels out:
\[ \text{Percentage Change} = \left( \frac{24}{25} \right) \times 100 = 96\% \]

### Final Answer:
The percentage change in the area of the circle is **96%**.

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