The volume of a vessel in the form of a right circular cylinder is `567 pi cm^(3)` and its height is 7 cm. The radius of its base is `:`

Options

A. 8 cm
B. 5 cm
C. 9 cm
D. 6 cm

Answer

To find the radius of the base of a right circular cylinder given its volume and height, 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: Substitute the given values into the formula.
We know:
- Volume \( V = 567 \pi \, \text{cm}^3 \)
- Height \( h = 7 \, \text{cm} \)

Substituting these values into the volume formula:
\[ 567 \pi = \pi r^2 \cdot 7 \]

### Step 3: Simplify the equation.
We can divide both sides of the equation by \( \pi \) (since \( \pi \) is not zero):
\[ 567 = r^2 \cdot 7 \]

### Step 4: Solve for \( r^2 \).
Now, divide both sides by 7 to isolate \( r^2 \):
\[ r^2 = \frac{567}{7} \]
Calculating the right side:
\[ r^2 = 81 \]

### Step 5: Find the radius \( r \).
To find \( r \), take the square root of both sides:
\[ r = \sqrt{81} \]
Calculating the square root:
\[ r = 9 \, \text{cm} \]

### Conclusion:
The radius of the base of the cylinder is \( 9 \, \text{cm} \).

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