A cuboidal metal of dimensions `44 cm xx30 cm xx15` cm was melted and cast into a cylinder of height 28 cm. Its radius is_____.

Options

A. 20 cm
B. 15 cm
C. 10 cm
D. 25 cm

Answer

To find the radius of the cylinder formed by melting a cuboidal metal, we will follow these steps:

### Step 1: Calculate the volume of the cuboid.
The volume \( V \) of a cuboid is given by the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
Substituting the given dimensions:
\[ V = 44 \, \text{cm} \times 30 \, \text{cm} \times 15 \, \text{cm} \]

### Step 2: Perform the multiplication.
Calculating the volume:
\[ V = 44 \times 30 = 1320 \, \text{cm}^2 \]
Now, multiply this result by the height:
\[ V = 1320 \times 15 = 19800 \, \text{cm}^3 \]

### Step 3: Set the volume of the cylinder equal to the volume of the cuboid.
The volume \( V \) of a cylinder is given by the formula:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cylinder. We know the height of the cylinder is 28 cm:
\[ 19800 = \pi r^2 \times 28 \]

### Step 4: Substitute the value of \( \pi \).
Using \( \pi \approx \frac{22}{7} \):
\[ 19800 = \frac{22}{7} r^2 \times 28 \]

### Step 5: Simplify the equation.
Rearranging gives:
\[ 19800 = \frac{22 \times 28}{7} r^2 \]
Calculating \( \frac{22 \times 28}{7} \):
\[ \frac{22 \times 28}{7} = \frac{616}{7} = 88 \]
So, we have:
\[ 19800 = 88 r^2 \]

### Step 6: Solve for \( r^2 \).
Dividing both sides by 88:
\[ r^2 = \frac{19800}{88} \]

### Step 7: Perform the division.
Calculating:
\[ r^2 = 225 \]

### Step 8: Find the radius \( r \).
Taking the square root of both sides:
\[ r = \sqrt{225} = 15 \, \text{cm} \]

Thus, the radius of the cylinder is **15 cm**.

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