Study the statements given below and decide which of the statements is/ are necessary to answer the given question?
What is the capacity of the cylindrical tank?
I. The area of the base is 61600 sq. cm.
II. The height of the tank is 1.5 times the radius.
III. The circumference of base is 880 cm.

Options

A. Only I and II
B. Only II and III
C. Only I and Ill
D. Only II and either I or III

Answer

To determine the capacity of the cylindrical tank, we need to find the volume of the cylinder, which is given by the formula:

\[ \text{Volume} = \pi r^2 h \]

Where:
- \( r \) is the radius of the base of the cylinder
- \( h \) is the height of the cylinder

### Step 1: Analyze the Statements

1. **Statement I**: The area of the base is \( 61600 \, \text{sq. cm} \).
- The area of the base of a cylinder is given by the formula:
\[ \text{Area} = \pi r^2 \]
- From this statement, we can find the radius \( r \) as follows:
\[ r^2 = \frac{\text{Area}}{\pi} = \frac{61600}{\pi} \]
- Thus, Statement I is necessary to find the radius.

2. **Statement II**: The height of the tank is \( 1.5 \) times the radius.
- This gives us a direct relationship between height and radius:
\[ h = 1.5r \]
- Therefore, Statement II is also necessary to find the height.

3. **Statement III**: The circumference of the base is \( 880 \, \text{cm} \).
- The circumference of the base is given by:
\[ \text{Circumference} = 2\pi r \]
- From this statement, we can find the radius \( r \) as follows:
\[ r = \frac{880}{2\pi} \]
- Thus, Statement III is also necessary to find the radius.

### Step 2: Determine Necessary Statements

To calculate the volume of the cylinder, we need both the radius \( r \) and the height \( h \).

- From **Statement I**, we can find the radius.
- From **Statement II**, we can find the height based on the radius.
- From **Statement III**, we can also find the radius.

### Conclusion

To determine the capacity of the cylindrical tank, we need:
- **Statement I** (Area of the base) or **Statement III** (Circumference of the base) to find the radius.
- **Statement II** (Height in terms of radius) is necessary to find the height.

Thus, the necessary statements to answer the question are:
- **Statement II** is essential, and either **Statement I** or **Statement III** is also required.

### Final Answer

The necessary statements are:
- **Statement II** (Height is 1.5 times the radius)
- Either **Statement I** (Area of the base) or **Statement III** (Circumference of the base).

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