The diameter of the base of a cylindrical drum is 35 dm and the height is 24 dm. It is full of kerosene. How many tins each of size `25 cm xx 22 cm xx 35 cm` can be filled with kerosene from the drum ?
(Use `pi = (22)/(7)`)

Options

A. a) 1200
B. b) 1020
C. c) 600
D. d) 120

Answer

To solve the problem of how many tins can be filled with kerosene from a cylindrical drum, we will follow these steps:

### Step 1: Calculate the Volume of the Cylindrical Drum
The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
Where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.

**Given:**
- Diameter of the base = 35 dm, so the radius \( r = \frac{35}{2} = 17.5 \) dm.
- Height \( h = 24 \) dm.

**Convert to centimeters:**
- \( r = 17.5 \) dm = \( 17.5 \times 10 = 175 \) cm.
- \( h = 24 \) dm = \( 24 \times 10 = 240 \) cm.

**Now, substitute the values into the volume formula:**
\[ V = \frac{22}{7} \times (175)^2 \times 240 \]

### Step 2: Calculate \( (175)^2 \)
\[ (175)^2 = 30625 \]

### Step 3: Substitute and Calculate the Volume
\[ V = \frac{22}{7} \times 30625 \times 240 \]
\[ V = \frac{22 \times 30625 \times 240}{7} \]

### Step 4: Calculate \( 22 \times 30625 \)
\[ 22 \times 30625 = 682750 \]

### Step 5: Calculate the Volume
\[ V = \frac{682750 \times 240}{7} \]
\[ V = \frac{163830000}{7} \approx 23404285.71 \text{ cm}^3 \]

### Step 6: Calculate the Volume of One Tin
The volume \( V_t \) of one tin is given by:
\[ V_t = \text{length} \times \text{breadth} \times \text{height} \]
**Given:**
- Length = 25 cm,
- Breadth = 22 cm,
- Height = 35 cm.

\[ V_t = 25 \times 22 \times 35 \]
\[ V_t = 19250 \text{ cm}^3 \]

### Step 7: Calculate the Number of Tins
Now, to find the number of tins \( n \) that can be filled with kerosene from the drum:
\[ n = \frac{V}{V_t} = \frac{23404285.71}{19250} \]

### Step 8: Calculate \( n \)
\[ n \approx 12150 \]

Thus, the number of tins that can be filled with kerosene from the drum is approximately **12150 tins**.

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