A rope makes 140 rounds of the circumference of a cylinder.the radius of whose base is 14 cm.How many time can it go round a cylinder with radiud 20 cm?

Options

A. 28
B. 17
C. 68
D. 200

Answer

To solve the problem step by step, we will use the concept of the circumference of a cylinder and the relationship between the radius and the number of rounds a rope can make.

### Step 1: Calculate the circumference of the first cylinder.
The formula for the circumference (C) of a circle is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius.

For the first cylinder with a radius of 14 cm:
\[ C_1 = 2 \pi \times 14 \]
\[ C_1 = 28 \pi \, \text{cm} \]

### Step 2: Calculate the total length of the rope.
Since the rope makes 140 rounds around the first cylinder, the total length of the rope (L) can be calculated as:
\[ L = \text{Number of rounds} \times \text{Circumference} \]
\[ L = 140 \times C_1 \]
\[ L = 140 \times 28 \pi \]
\[ L = 3920 \pi \, \text{cm} \]

### Step 3: Calculate the circumference of the second cylinder.
Now, we need to find the circumference of the second cylinder with a radius of 20 cm:
\[ C_2 = 2 \pi \times 20 \]
\[ C_2 = 40 \pi \, \text{cm} \]

### Step 4: Determine how many rounds the rope can make around the second cylinder.
To find the number of rounds (N) the rope can make around the second cylinder, we use the formula:
\[ N = \frac{\text{Total length of the rope}}{\text{Circumference of the second cylinder}} \]
\[ N = \frac{3920 \pi}{40 \pi} \]
\[ N = \frac{3920}{40} \]
\[ N = 98 \]

### Final Answer:
The rope can go around the cylinder with a radius of 20 cm **98 times**.

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