A rope makes 260 rounds of a cylinder with base radius 20 cm. How many times can it go round cylinder with base radius 26 cm?

Options

A. 130
B. 300
C. 200
D. 150

Answer

To solve the problem, we need to determine how many times the rope can wrap around a cylinder with a base radius of 26 cm, given that it makes 260 rounds around a cylinder with a base radius of 20 cm.

### Step-by-Step Solution:

1. **Calculate the Circumference of the First Cylinder (radius = 20 cm)**:
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2 \pi r \]
For the first cylinder with a radius of 20 cm:
\[ C_1 = 2 \pi \times 20 = 40 \pi \text{ cm} \]

2. **Calculate the Total Length of the Rope**:
Since the rope makes 260 rounds around the first cylinder, the total length of the rope \( L \) can be calculated as:
\[ L = \text{Number of rounds} \times \text{Circumference of the first cylinder} \]
\[ L = 260 \times 40 \pi = 10400 \pi \text{ cm} \]

3. **Calculate the Circumference of the Second Cylinder (radius = 26 cm)**:
Now, we calculate the circumference of the second cylinder with a radius of 26 cm:
\[ C_2 = 2 \pi \times 26 = 52 \pi \text{ cm} \]

4. **Determine the Number of Rounds Around the Second Cylinder**:
To find out how many rounds the rope can make around the second cylinder, we divide the total length of the rope by the circumference of the second cylinder:
\[ \text{Number of rounds} = \frac{L}{C_2} = \frac{10400 \pi}{52 \pi} \]
The \( \pi \) cancels out:
\[ \text{Number of rounds} = \frac{10400}{52} = 200 \]

### Final Answer:
The rope can go around the cylinder with a base radius of 26 cm **200 times**.