The radius of base and curved surface area of a right cylinder is 'r' units and `4pir h` square units respectively. The height of the cylinder is :

Options

A. `(h)/(2)` units
B. h units
C. 2 h units
D. 4 h units

Answer

To find the height of the cylinder given the radius and the curved surface area, 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:
\[ \text{Curved Surface Area} = 2\pi rh \]
where \( r \) is the radius of the base and \( h \) is the height of the cylinder.

### Step 2: Set up the equation
According to the question, the curved surface area is given as:
\[ 4\pi rh \]
We can set this equal to the formula for the curved surface area:
\[ 2\pi rh = 4\pi h \]

### Step 3: Simplify the equation
We can divide both sides of the equation by \( 2\pi \) (assuming \( \pi \neq 0 \)):
\[ rh = 2h \]

### Step 4: Solve for height \( h \)
To isolate \( h \), we can divide both sides by \( r \) (assuming \( r \neq 0 \)):
\[ h = \frac{2h}{r} \]

### Step 5: Rearranging the equation
Rearranging gives us:
\[ h = 2 \]

Thus, the height of the cylinder is:
\[ h = 2 \text{ units} \]

### Final Answer
The height of the cylinder is \( 2 \) units.

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