A hollow right circular cylinder with height 8 cm and base radius 7 cm is opened out into a rectangle What are the length and breadth of the rectangle respectively ?

Options

A. 22 cm, 16 cm
B. 44 cm, 8 cm
C. 22 cm, 8 cm
D. 44 cm, 16 cm

Answer

To find the dimensions of the rectangle formed when a hollow right circular cylinder is opened out, we need to determine the length and breadth of the rectangle based on the given dimensions of the cylinder.

### Step-by-Step Solution:

1. **Identify the dimensions of the cylinder**:
- Height (h) = 8 cm
- Base radius (r) = 7 cm

2. **Calculate the circumference of the base of the cylinder**:
The circumference of the base of the cylinder will become the length of the rectangle when the cylinder is opened out. The formula for the circumference (C) of a circle is:
\[ C = 2 \pi r \]
Substituting the value of r:
\[ C = 2 \times \frac{22}{7} \times 7 \]
Simplifying this:
\[ C = 2 \times 22 = 44 \text{ cm} \]
Thus, the length of the rectangle is 44 cm.

3. **Determine the breadth of the rectangle**:
The height of the cylinder remains the same when it is opened out, which becomes the breadth of the rectangle. Therefore:
\[ \text{Breadth} = \text{Height} = 8 \text{ cm} \]

4. **Final dimensions of the rectangle**:
- Length = 44 cm
- Breadth = 8 cm

### Conclusion:
The dimensions of the rectangle formed by opening out the hollow right circular cylinder are:
- Length = 44 cm
- Breadth = 8 cm