Height of a drinking glass is 14 cm, the diameters of its two circular ends are 4 cm and 2 cm, then the capacity of glass is:

Options

A. `102.67 cm^3`
B. `102.76 cm^3`
C. `202.66 cm^3`
D. `206.76 cm^3`

Answer

To find the capacity of the drinking glass, we can model it as a frustum of a cone. The formula for the volume \( V \) of a frustum of a cone is given by:

\[ V = \frac{1}{3} \pi h (R^2 + r^2 + Rr) \]

where:
- \( R \) is the radius of the larger base,
- \( r \) is the radius of the smaller base,
- \( h \) is the height of the frustum.

### Step 1: Identify the dimensions
Given:
- Height \( h = 14 \) cm
- Diameter of the larger base = 4 cm, thus \( R = \frac{4}{2} = 2 \) cm
- Diameter of the smaller base = 2 cm, thus \( r = \frac{2}{2} = 1 \) cm

### Step 2: Substitute the values into the formula
Now we will substitute the values of \( R \), \( r \), and \( h \) into the volume formula:

\[ V = \frac{1}{3} \pi (14) (2^2 + 1^2 + 2 \cdot 1) \]

### Step 3: Calculate the terms inside the parentheses
Calculating \( R^2 + r^2 + Rr \):

\[ R^2 = 2^2 = 4 \]
\[ r^2 = 1^2 = 1 \]
\[ Rr = 2 \cdot 1 = 2 \]

Adding these together:

\[ R^2 + r^2 + Rr = 4 + 1 + 2 = 7 \]

### Step 4: Substitute back into the volume formula
Now substituting back into the volume formula:

\[ V = \frac{1}{3} \pi (14) (7) \]

### Step 5: Simplify the expression
Calculating \( \frac{1}{3} \cdot 14 \cdot 7 \):

\[ V = \frac{1}{3} \cdot 98 \pi \]

### Step 6: Calculate the volume using \( \pi \approx \frac{22}{7} \)
Substituting \( \pi \) with \( \frac{22}{7} \):

\[ V = \frac{98}{3} \cdot \frac{22}{7} \]

### Step 7: Simplify further
Now simplifying:

\[ V = \frac{98 \cdot 22}{3 \cdot 7} = \frac{2156}{21} \]

### Step 8: Final calculation
Calculating \( \frac{2156}{21} \):

\[ V \approx 102.67 \text{ cm}^3 \]

### Conclusion
Thus, the capacity of the drinking glass is approximately \( 102.67 \text{ cm}^3 \).

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