If the curved surface area of a right circular cylinder is `88 cm^(2)` and its height is 14 cm, then what will be the diameter of base of a cylinder ?

Options

A. 2 cm
B. 3 cm
C. 4 cm
D. 5 cm

Answer

To find the diameter of the base of a right circular cylinder given its curved surface area and height, we can follow these steps:

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

### Step 2: Substitute the given values into the formula.
We know the curved surface area (CSA) is \( 88 \, \text{cm}^2 \) and the height \( h \) is \( 14 \, \text{cm} \). Plugging these values into the formula gives us:
\[ 88 = 2\pi r \times 14 \]

### Step 3: Simplify the equation.
Now, simplify the equation:
\[ 88 = 28\pi r \]

### Step 4: Solve for the radius \( r \).
To isolate \( r \), divide both sides by \( 28\pi \):
\[ r = \frac{88}{28\pi} \]

### Step 5: Calculate the radius.
Now, we can calculate the radius using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{88}{28 \times \frac{22}{7}} = \frac{88 \times 7}{28 \times 22} \]
Calculating this step-by-step:
- First, simplify \( \frac{88}{28} = \frac{22}{7} \)
- Now, substituting back:
\[ r = \frac{22 \times 7}{22} = 7 \, \text{cm} \]

### Step 6: Find the diameter.
The diameter \( d \) of the base of the cylinder is twice the radius:
\[ d = 2r = 2 \times 7 = 14 \, \text{cm} \]

### Final Answer:
The diameter of the base of the cylinder is \( 14 \, \text{cm} \).

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