The curved surface area of a right circular cylinder of height 28 cm is 176 `cm^2` . The volume( in `cm^3` ) of cylinder is (Take ` pi = (22)/(7)` )

Options

A. 66
B. 110
C. 88
D. 176

Answer

To find the volume of the right circular cylinder given its curved surface area (CSA) and height, we can follow these steps:

### Step 1: Write down the formula for the curved surface area of a cylinder.
The curved surface area (CSA) of a cylinder is given by the formula:
\[ \text{CSA} = 2 \pi r h \]
where \( r \) is the radius and \( h \) is the height of the cylinder.

### Step 2: Substitute the known values into the formula.
From the problem, we know:
- CSA = 176 cm²
- Height \( h = 28 \) cm
- \( \pi = \frac{22}{7} \)

Substituting these values into the CSA formula:
\[ 176 = 2 \times \frac{22}{7} \times r \times 28 \]

### Step 3: Simplify the equation to solve for \( r \).
First, simplify the right side:
\[ 176 = \frac{44}{7} \times r \times 28 \]
\[ 176 = \frac{1232}{7} \times r \]

Now, multiply both sides by 7 to eliminate the fraction:
\[ 176 \times 7 = 1232r \]
\[ 1232 = 1232r \]

### Step 4: Solve for \( r \).
Now, divide both sides by 1232:
\[ r = \frac{1232}{1232} = 1 \text{ cm} \]

### Step 5: Use the radius to find the volume of the cylinder.
The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
Substituting the known values:
\[ V = \frac{22}{7} \times (1)^2 \times 28 \]
\[ V = \frac{22}{7} \times 1 \times 28 \]

### Step 6: Simplify to find the volume.
\[ V = \frac{22 \times 28}{7} \]
Now, simplify:
\[ V = \frac{616}{7} = 88 \text{ cm}^3 \]

### Final Answer:
The volume of the cylinder is \( 88 \text{ cm}^3 \).

---