A rope makes 125 rounds of a cylinder with base radius 15 cm. How many times can it go round cylinder with base radius 25 cm ?

Options

A. 100
B. 75
C. 80
D. 65

Answer

To solve the problem, we need to determine how many times the rope can go around a cylinder with a base radius of 25 cm, given that it makes 125 rounds around a cylinder with a base radius of 15 cm.

### Step-by-Step Solution:

1. **Calculate the Circumference of the First Cylinder:**
The formula for the circumference \( C \) of a circle is given by:
\[ C = 2\pi r \]
For the first cylinder with a radius of 15 cm:
\[ C_1 = 2\pi \times 15 = 30\pi \text{ cm} \]

2. **Calculate the Total Length of the Rope:**
Since the rope makes 125 rounds around the first cylinder, the total length \( L \) of the rope can be calculated as:
\[ L = \text{Number of rounds} \times \text{Circumference of the first cylinder} \]
\[ L = 125 \times 30\pi = 3750\pi \text{ cm} \]

3. **Calculate the Circumference of the Second Cylinder:**
Now, we calculate the circumference of the second cylinder with a radius of 25 cm:
\[ C_2 = 2\pi \times 25 = 50\pi \text{ cm} \]

4. **Determine the Number of Rounds Around the Second Cylinder:**
To find out how many times the rope can go around the second cylinder, we divide the total length of the rope by the circumference of the second cylinder:
\[ \text{Number of rounds} = \frac{L}{C_2} = \frac{3750\pi}{50\pi} \]
The \( \pi \) cancels out:
\[ \text{Number of rounds} = \frac{3750}{50} = 75 \]

Thus, the rope can go around the cylinder with a base radius of 25 cm a total of **75 times**.