If the volume of a right circular cylinder is `9pi h m^(3)`, where h is its height (in metres) then the diameter of the base of the cylinder is equal to

Options

A. 3m
B. 6m
C. 9m
D. 12 m

Answer

To find the diameter of the base of a right circular cylinder given its volume, we can follow these steps:

### Step 1: Write down the formula for the volume of a cylinder.
The volume \( V \) of a right circular cylinder is given by the formula:
\[ V = \pi r^2 h \]
where \( r \) is the radius of the base and \( h \) is the height of the cylinder.

### Step 2: Set the given volume equal to the formula.
We are given that the volume of the cylinder is \( 9\pi h \) m³. Therefore, we can set up the equation:
\[ \pi r^2 h = 9\pi h \]

### Step 3: Simplify the equation.
Since \( h \) is common on both sides of the equation, we can cancel it out (assuming \( h \neq 0 \)):
\[ r^2 = 9 \]

### Step 4: Solve for the radius \( r \).
To find \( r \), we take the square root of both sides:
\[ r = \sqrt{9} = 3 \text{ m} \]

### Step 5: Calculate the diameter \( d \).
The diameter \( d \) of the base of the cylinder is twice the radius:
\[ d = 2r = 2 \times 3 = 6 \text{ m} \]

### Conclusion:
The diameter of the base of the cylinder is \( 6 \) meters.

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