The volume (in cu.com) of a righe circular cylinder with radius 2.5 cm and height 2 cm is : ( Take `pi = (22)/(7)` )

Options

A. 275
B. `275//21`
C. `275//2`
D. `275//7`

Answer

To find the volume of a right circular cylinder, we use the formula:

\[ V = \pi r^2 h \]

where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height, and
- \( \pi \) is a constant approximately equal to \( \frac{22}{7} \).

### Step 1: Identify the given values
- Radius \( r = 2.5 \) cm
- Height \( h = 2 \) cm
- \( \pi = \frac{22}{7} \)

### Step 2: Calculate \( r^2 \)
\[ r^2 = (2.5)^2 = 2.5 \times 2.5 = 6.25 \]

### Step 3: Substitute the values into the volume formula
\[ V = \pi r^2 h = \frac{22}{7} \times 6.25 \times 2 \]

### Step 4: Calculate \( 6.25 \times 2 \)
\[ 6.25 \times 2 = 12.5 \]

### Step 5: Substitute back into the volume formula
\[ V = \frac{22}{7} \times 12.5 \]

### Step 6: Convert \( 12.5 \) to a fraction
\[ 12.5 = \frac{125}{10} = \frac{25}{2} \]

### Step 7: Substitute \( 12.5 \) as a fraction into the volume formula
\[ V = \frac{22}{7} \times \frac{25}{2} \]

### Step 8: Multiply the fractions
\[ V = \frac{22 \times 25}{7 \times 2} = \frac{550}{14} \]

### Step 9: Simplify the fraction
\[ \frac{550}{14} = \frac{275}{7} \]

### Step 10: Final volume in cubic centimeters
Thus, the volume of the cylinder is:
\[ V = \frac{275}{7} \text{ cm}^3 \]

### Summary of the solution:
The volume of the right circular cylinder with radius 2.5 cm and height 2 cm is \( \frac{275}{7} \) cm³.

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