A steel cylinder of radius 3.5 cm and height 7 cm is melted to form bearings of radius 1 cm and thickness 8.75 mm. How many such bearings can be made ?

Options

A. 55
B. 47
C. 36
D. 64

Answer

To solve the problem, we need to find the volume of the original steel cylinder and the volume of one bearing. Then, we can determine how many bearings can be made from the melted steel.

### Step 1: Calculate the volume of the steel cylinder.

The formula for the volume \( V \) of a cylinder is given by:

\[ V = \pi r^2 h \]

Where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.

Given:
- Radius of the cylinder \( r = 3.5 \) cm,
- Height of the cylinder \( h = 7 \) cm.

Substituting the values:

\[ V = \pi (3.5)^2 (7) \]

Calculating \( (3.5)^2 \):

\[ (3.5)^2 = 12.25 \]

Now substituting back into the volume formula:

\[ V = \pi \times 12.25 \times 7 \]

Calculating \( 12.25 \times 7 \):

\[ 12.25 \times 7 = 85.75 \]

Thus, the volume of the cylinder is:

\[ V = 85.75\pi \text{ cm}^3 \]

### Step 2: Calculate the volume of one bearing.

The bearing is also a cylinder, and we can use the same formula for the volume of a cylinder.

Given:
- Radius of the bearing \( r = 1 \) cm,
- Thickness of the bearing \( h = 8.75 \) mm = \( 0.875 \) cm (since 1 cm = 10 mm).

Now substituting these values into the volume formula:

\[ V_{bearing} = \pi (1)^2 (0.875) \]

Calculating \( (1)^2 \):

\[ (1)^2 = 1 \]

Thus, the volume of one bearing is:

\[ V_{bearing} = \pi \times 1 \times 0.875 = 0.875\pi \text{ cm}^3 \]

### Step 3: Calculate the number of bearings that can be made.

To find the number of bearings, we divide the volume of the cylinder by the volume of one bearing:

\[ \text{Number of bearings} = \frac{V_{cylinder}}{V_{bearing}} = \frac{85.75\pi}{0.875\pi} \]

The \( \pi \) cancels out:

\[ \text{Number of bearings} = \frac{85.75}{0.875} \]

Calculating \( \frac{85.75}{0.875} \):

\[ \frac{85.75}{0.875} = 98 \]

### Final Answer:
The number of bearings that can be made is **98**.

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