An iron pillar has some part n the form of a right circular cylinder and remaining in the form of a right circular cone. The radius of base of cone , as well as cylinder is 21 cm . The cylindrical part is 80 cm high and conical part is 16 cm high . Find the weight of the pillar , if ` 1 cm^(3)` of iron weighs 8.45 g :

Options

A. 999.39 kg
B. 111 kg
C. 1001 kg
D. 989 kg

Answer

To solve the problem of finding the weight of the iron pillar, we need to calculate the total volume of the pillar, which consists of a cylindrical part and a conical part, and then use the density of iron to find the weight. Here’s the step-by-step solution:

### Step 1: Identify the dimensions
- Radius of the base (r) = 21 cm
- Height of the cylindrical part (h_cylinder) = 80 cm
- Height of the conical part (h_cone) = 16 cm

### Step 2: Calculate the volume of the cylindrical part
The formula for the volume of a cylinder is:
\[ V_{cylinder} = \pi r^2 h \]

Substituting the values:
\[ V_{cylinder} = \pi \times (21)^2 \times 80 \]

### Step 3: Calculate the volume of the conical part
The formula for the volume of a cone is:
\[ V_{cone} = \frac{1}{3} \pi r^2 h \]

Substituting the values:
\[ V_{cone} = \frac{1}{3} \pi \times (21)^2 \times 16 \]

### Step 4: Combine the volumes
The total volume of the pillar is the sum of the volumes of the cylinder and the cone:
\[ V_{total} = V_{cylinder} + V_{cone} \]

### Step 5: Factor out common terms
We can factor out \(\pi\) and \(21^2\):
\[ V_{total} = \pi \times (21)^2 \times (80 + \frac{1}{3} \times 16) \]

### Step 6: Calculate the expression inside the parentheses
Calculate \(80 + \frac{1}{3} \times 16\):
\[ \frac{1}{3} \times 16 = \frac{16}{3} \]
Convert \(80\) to a fraction:
\[ 80 = \frac{240}{3} \]
So,
\[ 80 + \frac{16}{3} = \frac{240 + 16}{3} = \frac{256}{3} \]

### Step 7: Substitute back into the volume formula
Now we have:
\[ V_{total} = \pi \times (21)^2 \times \frac{256}{3} \]

### Step 8: Calculate \(21^2\)
\[ 21^2 = 441 \]

### Step 9: Substitute and calculate the total volume
\[ V_{total} = \pi \times 441 \times \frac{256}{3} \]

Using \(\pi \approx \frac{22}{7}\):
\[ V_{total} = \frac{22}{7} \times 441 \times \frac{256}{3} \]

### Step 10: Simplify the calculation
Calculate:
\[ V_{total} = \frac{22 \times 441 \times 256}{21} \]

### Step 11: Calculate the weight of the pillar
The weight of the pillar can be found by multiplying the volume by the weight of 1 cm³ of iron:
Weight = Volume × Density
\[ \text{Weight} = V_{total} \times 8.45 \]

### Step 12: Convert weight to kilograms
Since the weight is calculated in grams, convert it to kilograms by dividing by 1000.

### Final Calculation
After calculating all the above steps, we find that the weight of the iron pillar is approximately 999.3984 kg.