Institution: Bangladesh Bank Exam: Officer (Cash) -Sonali Bank | BD Development | BD Krishi Bank - 12.10.2018 ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the problem, we need to establish two key relationships based on the given information about the circles.

Let \( r \) be the radius of the smaller circle and \( R \) the radius of the larger circle. We know:

1. The difference between radii:
\[ R - r = 14 \, \text{cm} \]
2. The difference between the areas:
\[ \pi R^2 - \pi r^2 = 1056 \, \text{cm}^2 \]
This can be simplified to:
\[ \pi (R^2 - r^2) = 1056 \]
Using the difference of squares, we rewrite it as:
\[ \pi (R - r)(R + r) = 1056 \]

Now substituting the first equation into the area equation, we have:
- \( R - r = 14 \)
- So, \( R + r \) can be expressed as \( R + r = (R - r) + 2r = 14 + 2r \).

Plugging this into the area equation gives:
\[ \pi \cdot 14 \cdot (14 + 2r) = 1056 \]
Simplifying, we find:
\[ 14\pi(14 + 2r) = 1056 \]
Dividing both sides by \( 14\pi \) yields:
\[ 14 + 2r = \frac{1056}{14\pi} \approx 24 \]
Thus,
\[ 2r = 24 - 14 = 10 \]
Therefore, \( r = 5 \, \text{cm} \).

Thus, the radius of the smaller circle is \( 5 \, \text{cm} \), which is option B.