A cylindrical tank with radius and height of 21.43 cm and 12 cm respectively is filled upto 80% of its capacity with alcohol. If total alcohol from cylindrical tank transferred into 30 cuboidal flask whose length and breadth is 7 cm & 3 cm respectively. Find the height of each cuboidal flask?

Options

A. 18 cm
B. 25 cm
C. 23 cm
D. 22 cm

Explanation

To solve the problem step by step, we need to follow these calculations:

### Step 1: Calculate the volume of the cylindrical tank.
The formula for the volume \( V \) of a cylinder is given by:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height.

Given:
- Radius \( r = 21.43 \) cm
- Height \( h = 12 \) cm

Substituting the values into the formula:
\[ V = \frac{22}{7} \times (21.43)^2 \times 12 \]

Calculating \( (21.43)^2 \):
\[ (21.43)^2 = 459.0649 \]

Now substituting:
\[ V = \frac{22}{7} \times 459.0649 \times 12 \]
\[ V = \frac{22 \times 459.0649 \times 12}{7} \]
\[ V = \frac{12164.2378}{7} \approx 1737.7483 \text{ cm}^3 \]

### Step 2: Calculate the volume of alcohol in the tank.
The tank is filled to 80% of its capacity:
\[ \text{Volume of alcohol} = 0.8 \times V \]
\[ \text{Volume of alcohol} = 0.8 \times 17320 \approx 13856 \text{ cm}^3 \]

### Step 3: Calculate the volume of one cuboidal flask.
The volume \( V_f \) of a cuboidal flask is given by:
\[ V_f = \text{length} \times \text{breadth} \times \text{height} \]
Given:
- Length \( l = 7 \) cm
- Breadth \( b = 3 \) cm
- Height \( h_f \) (unknown)

Substituting the known values:
\[ V_f = 7 \times 3 \times h_f = 21h_f \text{ cm}^3 \]

### Step 4: Calculate the total volume of 30 cuboidal flasks.
The total volume \( V_{total} \) of 30 flasks is:
\[ V_{total} = 30 \times V_f = 30 \times 21h_f = 630h_f \text{ cm}^3 \]

### Step 5: Set the volume of alcohol equal to the total volume of the flasks.
Since all the alcohol from the cylindrical tank is transferred to the flasks:
\[ 13856 = 630h_f \]

### Step 6: Solve for the height of each cuboidal flask.
\[ h_f = \frac{13856}{630} \approx 22 \text{ cm} \]

Thus, the height of each cuboidal flask is approximately **22 cm**.

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