The volume of a vessel is in the form of a right circular cylinder is 448 `pi cm^(3)` and its height is 7cm. The radius of its base is `:`

Options

A. 5cm
B. 7cm
C. 9 cm
D. 8 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-by-Step Solution:

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.

2. **Substitute the known values into the formula:**
We know that the volume \( V = 448\pi \, \text{cm}^3 \) and the height \( h = 7 \, \text{cm} \). Substituting these values into the formula gives:
\[ 448\pi = \pi r^2 \cdot 7 \]

3. **Cancel out \( \pi \) from both sides:**
Since \( \pi \) is present on both sides of the equation, we can cancel it out:
\[ 448 = r^2 \cdot 7 \]

4. **Solve for \( r^2 \):**
To isolate \( r^2 \), divide both sides of the equation by 7:
\[ r^2 = \frac{448}{7} \]

5. **Calculate \( \frac{448}{7} \):**
Performing the division:
\[ r^2 = 64 \]

6. **Take the square root to find \( r \):**
Now, take the square root of both sides to find \( r \):
\[ r = \sqrt{64} = 8 \, \text{cm} \]

### Final Answer:
The radius of the base of the cylinder is \( 8 \, \text{cm} \).