The difference between Circumference of circle A and diameter is 60 cm. If Radius of Circle Bis 6 cm less than circle A then find area of Circle B?

Options

A. `222 cm^2`
B. `201 cm^2`
C. `248 cm^2`
D. `250cm^2`

Explanation

To solve the problem step by step, let's break it down:

### Step 1: Understand the relationship between circumference and diameter
The circumference \( C \) of a circle is given by the formula:
\[ C = 2\pi r \]
where \( r \) is the radius of the circle. The diameter \( d \) is given by:
\[ d = 2r \]
According to the problem, the difference between the circumference of Circle A and its diameter is 60 cm:
\[ C - d = 60 \text{ cm} \]

### Step 2: Substitute the formulas for circumference and diameter
Substituting the formulas into the equation, we have:
\[ 2\pi r - 2r = 60 \]

### Step 3: Factor out the common term
We can factor out \( 2r \):
\[ 2r(\pi - 1) = 60 \]

### Step 4: Solve for the radius \( r \) of Circle A
Now, we can solve for \( r \):
\[ r(\pi - 1) = 30 \]
\[ r = \frac{30}{\pi - 1} \]

### Step 5: Calculate the numerical value of \( r \)
Using \( \pi \approx 3.14 \):
\[ r \approx \frac{30}{3.14 - 1} = \frac{30}{2.14} \approx 14.02 \text{ cm} \]
For simplicity, we can round this to \( r = 14 \text{ cm} \).

### Step 6: Find the radius of Circle B
According to the problem, the radius of Circle B is 6 cm less than that of Circle A:
\[ r_B = r_A - 6 = 14 - 6 = 8 \text{ cm} \]

### Step 7: Calculate the area of Circle B
The area \( A \) of a circle is given by the formula:
\[ A = \pi r^2 \]
Substituting the radius of Circle B:
\[ A_B = \pi (8)^2 = 64\pi \]

### Step 8: Calculate the numerical value of the area
Using \( \pi \approx 3.14 \):
\[ A_B \approx 64 \times 3.14 \approx 200.96 \text{ cm}^2 \]
For simplicity, we can round this to \( 201 \text{ cm}^2 \).

### Final Answer
The area of Circle B is approximately \( 201 \text{ cm}^2 \).

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