The problem shows a circular area with a diameter of 14 cm containing two smaller circles with a radius of $\frac{7}{4} \, \text{cm}$ each. It likely involves finding an area difference or some similar calculation based on the geometry provided.

Let me analyze and solve it step by step:

Step 1: Find the area of the large circle

The radius of the large circle is: $\text{Radius} = \frac{\text{Diameter}}{2} = \frac{14}{2} = 7 \, \text{cm}.$

The area of a circle is given by: $\text{Area} = \pi r^2.$

For the large circle: $\text{Area}_{\text{large}} = \pi (7)^2 = 49\pi \, \text{cm}^2.$

Step 2: Find the area of one smaller circle

The radius of a smaller circle is given as $\frac{7}{4} \, \text{cm}$. The area of one smaller circle is: $\text{Area}_{\text{small}} = \pi \left( \frac{7}{4} \right)^2 = \pi \cdot \frac{49}{16} = \frac{49\pi}{16} \, \text{cm}^2.$

Step 3: Find the total area of the two smaller circles

There are two smaller circles, so the total area is: $\text{Total Area}_{\text{small}} = 2 \cdot \frac{49\pi}{16} = \frac{98\pi}{16} = \frac{49\pi}{8} \, \text{cm}^2.$

Step 4: Find the shaded area

The shaded area is the area of the large circle minus the total area of the two smaller circles: $\text{Shaded Area} = \text{Area}_{\text{large}} - \text{Total Area}_{\text{small}}.$

Substituting the values: $\text{Shaded Area} = 49\pi - \frac{49\pi}{8}.$

Simplify: $\text{Shaded Area} = \frac{392\pi}{8} - \frac{49\pi}{8} = \frac{343\pi}{8} \, \text{cm}^2.$

Final Answer:

The shaded area is: $\boxed{\frac{343\pi}{8} \, \text{cm}^2} \quad \text{or approximately } 134.97 \, \text{cm}^2 \, \text{(using } \pi \approx 3.14\text{)}.$

Would you like me to explain any specific step or provide further details?

Related Questions:

1. What would the shaded area be if the radius of the large circle were doubled?
2. How does the shaded area change if there were three smaller circles instead of two?
3. What fraction of the large circle's area is taken up by the smaller circles?
4. Can you derive a formula for the shaded area if the radius of the smaller circles is a variable?
5. How does the total area calculation change if the smaller circles overlap?

Tip:

Always ensure the units of radius and diameter are consistent before starting calculations!