Find the increase in circumference of a circle of radius 14 cm, if the radius is increased by 7 cm. `(pi = (22)/(7))`

Options

A. 44 cm
B. 22 cm
C. 66 cm
D. 88 cm

Answer

To find the increase in the circumference of a circle when the radius is increased, we can follow these steps:

### Step 1: Calculate the Old Circumference (C1)
The formula for the circumference of a circle is given by:
\[ C = 2 \pi r \]
Where \( r \) is the radius of the circle.

Given the old radius \( r = 14 \) cm, we can substitute this value into the formula:
\[ C_1 = 2 \times \frac{22}{7} \times 14 \]

### Step 2: Simplify the Calculation for C1
Now, let's perform the calculations:
\[ C_1 = 2 \times \frac{22}{7} \times 14 = \frac{2 \times 22 \times 14}{7} \]
Calculating \( 2 \times 22 = 44 \) and then \( 44 \times 14 = 616 \):
\[ C_1 = \frac{616}{7} \]
Now, dividing \( 616 \) by \( 7 \):
\[ C_1 = 88 \text{ cm} \]

### Step 3: Calculate the New Circumference (C2)
Now, if the radius is increased by \( 7 \) cm, the new radius \( r \) will be:
\[ r = 14 + 7 = 21 \text{ cm} \]
Using the circumference formula again:
\[ C_2 = 2 \pi r = 2 \times \frac{22}{7} \times 21 \]

### Step 4: Simplify the Calculation for C2
Perform the calculations:
\[ C_2 = 2 \times \frac{22}{7} \times 21 = \frac{2 \times 22 \times 21}{7} \]
Calculating \( 2 \times 22 = 44 \) and then \( 44 \times 21 = 924 \):
\[ C_2 = \frac{924}{7} \]
Now, dividing \( 924 \) by \( 7 \):
\[ C_2 = 132 \text{ cm} \]

### Step 5: Calculate the Increase in Circumference
To find the increase in circumference, we subtract the old circumference from the new circumference:
\[ \text{Increase} = C_2 - C_1 = 132 - 88 \]
Calculating this gives:
\[ \text{Increase} = 44 \text{ cm} \]

### Final Answer
The increase in circumference is \( 44 \text{ cm} \).

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