The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters `36 cm` and `20 cm` is

Options

A. 56 cm
B. 42 cm
C. 28 cm
D. 16 cm

Explanation

To find the radius of a circle whose circumference is equal to the sum of the circumferences of two circles with diameters of 36 cm and 20 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Calculate the Circumference of the First Circle:**
The diameter of the first circle is 36 cm. The formula for the circumference (C) of a circle is:
\[ C = \pi \times d \]
Therefore, the circumference of the first circle is:
\[ C_1 = \pi \times 36 \]

2. **Calculate the Circumference of the Second Circle:**
The diameter of the second circle is 20 cm. Using the same formula for circumference:
\[ C_2 = \pi \times 20 \]

3. **Sum the Circumferences of Both Circles:**
Now, we add the circumferences of the two circles:
\[ C_{total} = C_1 + C_2 = \pi \times 36 + \pi \times 20 \]
Factoring out \(\pi\):
\[ C_{total} = \pi \times (36 + 20) = \pi \times 56 \]

4. **Set the Total Circumference Equal to the Circumference of the New Circle:**
Let the radius of the new circle be \(r\). The circumference of this circle is given by:
\[ C_{new} = 2\pi r \]
Setting the two circumferences equal gives us:
\[ 2\pi r = \pi \times 56 \]

5. **Solve for the Radius \(r\):**
Dividing both sides by \(\pi\) (assuming \(\pi \neq 0\)):
\[ 2r = 56 \]
Now, divide both sides by 2:
\[ r = \frac{56}{2} = 28 \text{ cm} \]

### Final Answer:
The radius of the circle is **28 cm**.

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