The volume of a cylinder is 2200 `cm^(3)` and its height is 7 cm. Then, the radius of the cylinder is ……… cm.

Options

A. 5
B. 15
C. 10
D. 20

Answer

To find the radius of the 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**:
\[ V = \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.

2. **Substitute the known values into the formula**:
Given that the volume \( V = 2200 \, \text{cm}^3 \) and the height \( h = 7 \, \text{cm} \), we can substitute these values into the formula:
\[ 2200 = \pi r^2 \cdot 7 \]

3. **Rearrange the equation to solve for \( r^2 \)**:
First, divide both sides by 7:
\[ \frac{2200}{7} = \pi r^2 \]
Now, calculate \( \frac{2200}{7} \):
\[ \frac{2200}{7} \approx 314.2857 \]
So, we have:
\[ \pi r^2 \approx 314.2857 \]

4. **Substitute the value of \( \pi \)**:
We can use \( \pi \approx \frac{22}{7} \) for our calculations:
\[ \frac{22}{7} r^2 \approx 314.2857 \]

5. **Multiply both sides by \( \frac{7}{22} \)** to isolate \( r^2 \):
\[ r^2 \approx 314.2857 \cdot \frac{7}{22} \]
Calculate \( 314.2857 \cdot \frac{7}{22} \):
\[ r^2 \approx 100 \]

6. **Take the square root to find \( r \)**:
\[ r = \sqrt{100} = 10 \, \text{cm} \]

### Final Answer:
The radius of the cylinder is \( 10 \, \text{cm} \).

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