The volume of a right circular cylinder, 14 cm in height, is equal to that of a cube whose edge is 11 cm. Taking `pi = (22)/(7)` the radius of the base of the cylinder is

Options

A. 5.2 cm
B. 5.5 cm
C. 11.0 cm
D. 22.0 cm

Answer

To find the radius of the base of the cylinder, we will follow these steps:

### Step 1: Calculate the Volume of the Cube
The volume \( V \) of a cube with edge length \( L \) is given by the formula:
\[ V = L^3 \]
Given that the edge length \( L = 11 \) cm, we can calculate the volume of the cube:
\[ V = 11^3 = 11 \times 11 \times 11 = 1331 \text{ cm}^3 \]

### Step 2: Write the Volume Formula for the 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 3: Substitute the Known Values into the Cylinder Volume Formula
We know the height \( h = 14 \) cm and \( \pi = \frac{22}{7} \). Therefore, we can write:
\[ V = \frac{22}{7} r^2 \times 14 \]

### Step 4: Set the Volumes Equal
Since the volume of the cube is equal to the volume of the cylinder, we set the two volumes equal to each other:
\[ 1331 = \frac{22}{7} r^2 \times 14 \]

### Step 5: Simplify the Right Side
First, simplify the right side:
\[ \frac{22}{7} \times 14 = \frac{22 \times 14}{7} = \frac{308}{7} \]
So we have:
\[ 1331 = \frac{308}{7} r^2 \]

### Step 6: Solve for \( r^2 \)
To isolate \( r^2 \), multiply both sides by \( 7 \):
\[ 1331 \times 7 = 308 r^2 \]
Calculating the left side:
\[ 9317 = 308 r^2 \]
Now, divide both sides by \( 308 \):
\[ r^2 = \frac{9317}{308} \]

### Step 7: Calculate \( r^2 \)
Now, we can perform the division:
\[ r^2 = 30.25 \]

### Step 8: Find \( r \)
To find \( r \), take the square root of \( r^2 \):
\[ r = \sqrt{30.25} = 5.5 \text{ cm} \]

### Final Answer
The radius of the base of the cylinder is \( 5.5 \) cm.

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