What is the volume of water required to fill `2//3^(rd)` of a cylindrical tank whose height is 18cm and radius is 2cm?

Options

A. `48pi cm^(3)`
B. `36 pi cm^(3)`
C. `96 pi cm^(3)`
D. `20 pi cm^(3)`

Answer

To find the volume of water required to fill \( \frac{2}{3} \) of a cylindrical tank with a height of 18 cm and a radius of 2 cm, we can follow these steps:

### 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.

### Step 2: Substitute the values into the formula
Here, the radius \( r = 2 \) cm and the height \( h = 18 \) cm. Substituting these values into the formula:

\[ V = \pi (2)^2 (18) \]

### Step 3: Calculate \( r^2 \)
Calculate \( r^2 \):

\[ (2)^2 = 4 \]

### Step 4: Substitute \( r^2 \) back into the volume formula
Now substitute \( r^2 \) back into the volume formula:

\[ V = \pi \times 4 \times 18 \]

### Step 5: Calculate \( 4 \times 18 \)
Now calculate \( 4 \times 18 \):

\[ 4 \times 18 = 72 \]

### Step 6: Write the volume in terms of \( \pi \)
Now we can write the volume of the cylindrical tank:

\[ V = 72\pi \, \text{cm}^3 \]

### Step 7: Calculate \( \frac{2}{3} \) of the volume
To find the volume of water required to fill \( \frac{2}{3} \) of the tank, we multiply the total volume by \( \frac{2}{3} \):

\[ \text{Volume of water} = \frac{2}{3} \times 72\pi \]

### Step 8: Simplify the expression
Now simplify the expression:

\[ \text{Volume of water} = \frac{2 \times 72\pi}{3} = \frac{144\pi}{3} = 48\pi \, \text{cm}^3 \]

### Final Answer
Thus, the volume of water required to fill \( \frac{2}{3} \) of the cylindrical tank is:

\[ \boxed{48\pi \, \text{cm}^3} \]

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