A cuboid having dimensions `16mxx11mxx8m` is melted to form a cylinder of radius 4 m. What is the height of the cylinder?

Options

A. 28 m
B. 14 m
C. 21 m
D. 32 m

Answer

To find the height of the cylinder formed by melting the cuboid, we need to follow these steps:

### Step 1: Calculate the Volume of the Cuboid
The volume \( V_c \) of a cuboid is given by the formula:
\[ V_c = \text{Length} \times \text{Breadth} \times \text{Height} \]
Given dimensions:
- Length \( L = 16 \, \text{m} \)
- Breadth \( B = 11 \, \text{m} \)
- Height \( H = 8 \, \text{m} \)

Substituting the values:
\[ V_c = 16 \times 11 \times 8 \]
Calculating this:
\[ V_c = 16 \times 11 = 176 \]
\[ V_c = 176 \times 8 = 1408 \, \text{m}^3 \]

### Step 2: Write the Volume Formula for the Cylinder
The volume \( V_{cl} \) of a cylinder is given by the formula:
\[ V_{cl} = \pi r^2 h \]
Where:
- \( r \) is the radius of the cylinder
- \( h \) is the height of the cylinder

Given radius:
- \( r = 4 \, \text{m} \)

Substituting the radius into the formula:
\[ V_{cl} = \pi \times (4)^2 \times h = \pi \times 16 \times h \]

### Step 3: Set the Volumes Equal
Since the volume of the cuboid is equal to the volume of the cylinder:
\[ V_c = V_{cl} \]
Substituting the volumes:
\[ 1408 = \pi \times 16 \times h \]

### Step 4: Solve for the Height \( h \)
Rearranging the equation to solve for \( h \):
\[ h = \frac{1408}{\pi \times 16} \]
Calculating \( \pi \) as \( \frac{22}{7} \):
\[ h = \frac{1408}{\frac{22}{7} \times 16} \]
This simplifies to:
\[ h = \frac{1408 \times 7}{22 \times 16} \]
Calculating the denominator:
\[ 22 \times 16 = 352 \]
Now substituting back:
\[ h = \frac{1408 \times 7}{352} \]
Calculating \( 1408 \div 352 \):
\[ 1408 \div 352 = 4 \]
Thus:
\[ h = 4 \times 7 = 28 \, \text{m} \]

### Final Answer
The height of the cylinder is \( h = 28 \, \text{m} \).

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