Read the statements carefully and select the correct option.
Statement-I : A rectangular tank is 80 m long and 25 m broad. Water flows into it through a pipe whose cross-section is `25" cm"^2`, at the rate of 16 km per hour. The rise in the level of water in the tank in 45 minutes is 2.5 cm.
Statement-II : If V is the volume of cuboid of dimensions a, b and c and A is its surface area, then `(A)/(V) =2 [a + b+c]`.

Options

A. Statement-I is true but Statement-II is false.
B. Statement-I is false but Statement-II is true.
C. Both Statement-I and Statement-II are true.
D. Both Statement-I and Statement-II are false.

Answer

To solve the problem, we will analyze both statements and determine their validity step by step.

### Step 1: Analyze Statement I
We have a rectangular tank with the following dimensions:
- Length (L) = 80 m
- Breadth (B) = 25 m

Water flows into the tank through a pipe with a cross-sectional area of 25 cm² at a rate of 16 km/h. We need to find out if the rise in water level in 45 minutes is indeed 2.5 cm.

#### Step 1.1: Convert units
First, convert the cross-sectional area of the pipe from cm² to m²:
- 25 cm² = 25 / 10000 m² = 0.0025 m²

Next, convert the flow rate from km/h to m/s:
- 16 km/h = (16 * 1000) / (60 * 60) m/s = 4.44 m/s

#### Step 1.2: Calculate the volume of water flowing into the tank
Now, calculate the volume of water that flows into the tank in 45 minutes:
- Time in seconds = 45 minutes * 60 seconds/minute = 2700 seconds
- Volume of water (V) = Flow rate (in m/s) * Cross-sectional area (in m²) * Time (in seconds)
- V = 4.44 m/s * 0.0025 m² * 2700 s = 30 m³

#### Step 1.3: Calculate the rise in water level
Now, we need to calculate the rise in water level in the tank:
- Volume of water = Length * Breadth * Height of water rise
- 30 m³ = 80 m * 25 m * Height
- Height = 30 m³ / (80 m * 25 m) = 30 / 2000 = 0.015 m = 1.5 cm

Since the calculated rise in water level (1.5 cm) is not equal to the stated rise (2.5 cm), Statement I is **incorrect**.

### Step 2: Analyze Statement II
Statement II states that if V is the volume of a cuboid with dimensions a, b, and c, and A is its surface area, then \( \frac{A}{V} = 2(a + b + c) \).

#### Step 2.1: Write the formulas
- Volume (V) = a * b * c
- Surface Area (A) = 2(ab + ac + bc)

#### Step 2.2: Calculate \( \frac{A}{V} \)
Now, we calculate \( \frac{A}{V} \):
- \( \frac{A}{V} = \frac{2(ab + ac + bc)}{abc} \)

#### Step 2.3: Simplify the expression
This simplifies to:
- \( \frac{A}{V} = 2 \left( \frac{ab + ac + bc}{abc} \right) = 2 \left( \frac{1}{c} + \frac{1}{b} + \frac{1}{a} \right) \)

This does not equal \( 2(a + b + c) \). Therefore, Statement II is also **incorrect**.

### Conclusion
Both Statement I and Statement II are incorrect.

### Final Answer
Both statements are false.