Find the capacity of a glass which is in the shape of frustum of height 14 cm and diameters of both circular ends are 4 cm and 2 cm.

Options

A. 308/3 `cm^(3)`
B. 298/21 `cm^(3)`
C. 112 `cm^(3)`
D. 398/21 `cm^(3)`

Answer

To find the capacity of the glass in the shape of a frustum, we will calculate the volume using the formula for the volume of a frustum of a cone.

### Step-by-Step Solution:

1. **Identify the given dimensions**:
- Height (h) of the frustum = 14 cm
- Diameter of the top circular end (D1) = 4 cm, so the radius (R1) = D1/2 = 4/2 = 2 cm
- Diameter of the bottom circular end (D2) = 2 cm, so the radius (R2) = D2/2 = 2/2 = 1 cm

2. **Use the volume formula for a frustum**:
The volume \( V \) of a frustum of a cone is given by the formula:
\[ V = \frac{1}{3} \pi h (R_1^2 + R_1 R_2 + R_2^2) \]

3. **Substitute the values into the formula**:
- \( R_1 = 2 \) cm
- \( R_2 = 1 \) cm
- \( h = 14 \) cm
- Using \( \pi \approx \frac{22}{7} \)

Now substituting the values:
\[ V = \frac{1}{3} \times \frac{22}{7} \times 14 \times (2^2 + 2 \times 1 + 1^2) \]

4. **Calculate \( R_1^2 + R_1 R_2 + R_2^2 \)**:
- \( R_1^2 = 2^2 = 4 \)
- \( R_1 R_2 = 2 \times 1 = 2 \)
- \( R_2^2 = 1^2 = 1 \)
- Therefore, \( R_1^2 + R_1 R_2 + R_2^2 = 4 + 2 + 1 = 7 \)

5. **Substitute back into the volume formula**:
\[ V = \frac{1}{3} \times \frac{22}{7} \times 14 \times 7 \]

6. **Simplify the expression**:
- The \( 7 \) in the numerator and denominator cancels out:
\[ V = \frac{1}{3} \times 22 \times 14 \]

7. **Calculate the final volume**:
- First calculate \( 22 \times 14 = 308 \)
- Then divide by 3:
\[ V = \frac{308}{3} \text{ cm}^3 \]

### Final Answer:
The capacity of the glass is \( \frac{308}{3} \) cm³ or approximately 102.67 cm³.