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

Options

A. 8 c m
B. 10 cm
C. 6 cm
D. 12 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 volume formula gives:
\[ 448\pi = \pi r^2 \cdot 7 \]

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

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

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

6. **Find \( r \) by taking the square root of both sides.**
To find the radius \( r \), take the square root of \( r^2 \):
\[ r = \sqrt{64} \]

7. **Calculate the square root.**
The square root of 64 is:
\[ r = 8 \, \text{cm} \]

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