Curved surface area of a cylinder is 110`cm^(2)` . If the height of cylinder is 5 cm, then what will be the diameter of its base?

Options

A. 14 cm
B. 7 cm
C. 3.5 cm
D. 10.5 cm

Answer

To find the diameter of the base of the 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 cylinder is given by:
\[ \text{CSA} = 2 \pi r h \]
where \( r \) is the radius and \( h \) is the height of the cylinder.

### Step 2: Substitute the known values into the formula.
We know the curved surface area is \( 110 \, \text{cm}^2 \) and the height \( h \) is \( 5 \, \text{cm} \). Substituting these values into the formula:
\[ 110 = 2 \pi r \times 5 \]

### Step 3: Simplify the equation.
First, we can simplify the equation:
\[ 110 = 10 \pi r \]

### Step 4: Solve for \( r \).
Now, we can isolate \( r \):
\[ r = \frac{110}{10 \pi} \]
Using \( \pi \approx \frac{22}{7} \):
\[ r = \frac{110}{10 \times \frac{22}{7}} = \frac{110 \times 7}{10 \times 22} \]
\[ r = \frac{770}{220} = \frac{7}{2} \, \text{cm} \]

### Step 5: Calculate the diameter.
The diameter \( d \) of the base of the cylinder is twice the radius:
\[ d = 2r = 2 \times \frac{7}{2} = 7 \, \text{cm} \]

### Final Answer:
The diameter of the base of the cylinder is \( 7 \, \text{cm} \).

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